# 3.5 Solve uniform motion applications  (Page 2/7)

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Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.

Wayne 21 mph, Dennis 28 mph

Jeromy can drive from his house in Cleveland to his college in Chicago in 4.5 hours. It takes his mother 6 hours to make the same drive. Jeromy drives 20 miles per hour faster than his mother. Find Jeromy’s speed and his mother’s speed.

Jeromy 80 mph, mother 60 mph

In [link] , the last example, we had two trains traveling the same distance. The diagram and the chart helped us write the equation we solved. Let’s see how this works in another case.

Christopher and his parents live 115 miles apart. They met at a restaurant between their homes to celebrate his mother’s birthday. Christopher drove 1.5 hours while his parents drove 1 hour to get to the restaurant. Christopher’s average speed was 10 miles per hour faster than his parents’ average speed. What were the average speeds of Christopher and of his parents as they drove to the restaurant?

## Solution

Step 1. Read the problem. Make sure all the words and ideas are understood.

• Draw a diagram to illustrate what it happening. Below shows a sketch of what is happening in the example.

• Create a table to organize the information.
• Label the columns rate, time, distance.
• List the two scenarios.
• Write in the information you know.

Step 2. Identify what we are looking for.

• We are asked to find the average speeds of Christopher and his parents.

Step 3. Name what we are looking for. Choose a variable to represent that quantity.

• Complete the chart.
• Use variable expressions to represent that quantity in each row.
• We are looking for their average speeds. Let’s let r represent the average speed of the parents. Since the Christopher’s speed is 10 mph faster, we represent that as $r+10.$

Fill in the speeds into the chart.

Multiply the rate times the time to get the distance.

Step 4. Translate into an equation.

• Restate the problem in one sentence with all the important information.
• Then, translate the sentence into an equation.
• Again, we need to identify a relationship between the distances in order to write an equation. Look at the diagram we created above and notice the relationship between the distance Christopher traveled and the distance his parents traveled.

The distance Christopher travelled plus the distance his parents travel must add up to 115 miles. So we write:

Step 5. Solve the equation using good algebra techniques.

$\begin{array}{cccc}\text{Now solve this equation.}\hfill & & & \hfill \begin{array}{ccc}\hfill 1.5\left(r+10\right)+r& =\hfill & 115\hfill \\ \hfill 1.5r+15+r& =\hfill & 115\hfill \\ \hfill 2.5r+15& =\hfill & 115\hfill \\ \hfill 2.5r& =\hfill & 100\hfill \\ \hfill r& =\hfill & 40\hfill \end{array}\hfill \\ & & & \text{So the parents’ speed was 40 mph.}\hfill \\ \text{Christopher’s speed is}\phantom{\rule{0.2em}{0ex}}r+10.\hfill & & & \hfill \begin{array}{c}\hfill r+10\hfill \\ \hfill 40+10\hfill \\ \hfill 50\hfill \end{array}\hfill \\ & & & \text{Christopher’s speed was 50 mph.}\hfill \end{array}$

Step 6. Check the answer in the problem and make sure it makes sense.

$\begin{array}{cccccc}\phantom{\rule{2.7em}{0ex}}\text{Christopher drove}\hfill & & & \text{50 mph (1.5 hours)}\hfill & =\hfill & \text{75 miles}\hfill \\ \phantom{\rule{2.7em}{0ex}}\text{His parents drove}\hfill & & & \text{40 mph (1 hours)}\hfill & =\hfill & \underset{\text{_______}}{\text{40 miles}}\hfill \\ & & & & & \text{115 miles}\hfill \end{array}$

$\begin{array}{cccc}\begin{array}{c}\mathbf{\text{Step 7. Answer}}\phantom{\rule{0.2em}{0ex}}\text{the question with a complete sentence.}\hfill \\ \\ \end{array}\hfill & & & \begin{array}{c}\text{Christopher’s speed was 50 mph.}\hfill \\ \text{His parents’ speed was 40 mph.}\hfill \end{array}\hfill \end{array}$

write in this form a/b answer should be in the simplest form 5%
convert to decimal 9/11
August
Equation in the form of a pending point y+2=1/6(×-4)
write in simplest form 3 4/2
August
From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
Melissa
what is the answer of w-2.6=7.55
10.15
Michael
w = 10.15 You add 2.6 to both sides and then solve for w (-2.6 zeros out on the left and leaves you with w= 7.55 + 2.6)
Korin
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her$66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?
x > $110,000 bruce greater than$110,000
Michael
Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost$4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use? nawal Reply$1.38 worth of strawberries + $1.14 worth of blueberries which=$2.52
Leitha
how
Zaione
is it right😊
Leitha
lol maybe
Robinson
8 pound of blueberries and 22 pounds of strawberries
Melissa
8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound
Melissa
8 pounds x 4.5 equal 36 22 pounds x 1.80 equal 39.60 36 + 39.60 equal 75.60 75.60 / 30 equal average 2.52 per pound
Melissa
hmmmm...... ?
Robinson
8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound
Melissa
The question asks how many pounds of each in order for her to have an average cost of $2.52. She needs 30 lb in all so 30 pounds times$2.52 equals $75.60. that's how much money she is spending on the fruit. That means she would need 8 pounds of blueberries and 22 lbs of strawberries to equal 75.60 Melissa good Robinson 👍 Leitha thanks Melissa. Leitha nawal let's do another😊 Leitha we can't use emojis...I see now Leitha Sorry for the multi post. My phone glitches. Melissa Vina has$4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin does she have?
10 quarters 16 dimes 12 nickels
Leitha
A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet.
wtf. is a tail wind or headwind?
Robert
48 miles per hour with headwind and 68 miles per hour with tailwind
Leitha
average speed is 58 mph
Leitha
Into the wind (headwind), 125 mph; with wind (tailwind), 175 mph. Use time (t) = distance (d) ÷ rate (r). since t is equal both problems, then 1210/(x-25) = 1694/(×+25). solve for x gives x=150.
bruce
the jet will fly 9.68 hours to cover either distance
bruce
Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs$3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound? Vonna Reply 33.336 Robinson Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost$8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be$10 per square foot?
Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have? mikayla Reply 2q=n ((2q).05) + ((q).25) = 8.75 .1q + .25q = 8.75 .35q = 8.75 q = 25 quarters 2(q) 2 (25) = 50 nickles Answer check 25 x .25 = 6.25 50 x .05 = 2.50 6.25 + 2.50 = 8.75 Melissa John has$175 in $5 and$10 bills in his drawer. The number of $5 bills is three times the number of$10 bills. How many of each are in the drawer?
7-$10 21-$5
Robert
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the$4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total \$23,500? (Round your answer to the nearest tenth of a percent.)
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
8mph
michele
16mph
Robert
3.8 mph
Ped
16 goes into 80 5times while 20 goes into 80 4times and is 4mph faster
Robert
what is the answer for this 3×9+28÷4-8
315
lashonna
how do you do xsquard+7x+10=0
What
(x + 2)(x + 5), then set each factor to zero and solve for x. so, x = -2 and x = -5.
bruce
I skipped it
What