



Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He covered a total distance of 51 miles. His speed when biking was 1.6 times his speed when running. Find Cruz’s biking and running speeds.
biking 16 mph, running 10 mph
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Phuong left home on his bicycle at 10:00. He rode on the flat street until 11:15, then rode uphill until 11:45. He rode a total of 31 miles. His speed riding uphill was 0.6 times his speed on the flat street. Find his speed biking uphill and on the flat street.
uphill 12 mph, flat street 20 mph
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Key concepts

Distance, Rate, and Time

D =
rt where
D = distance,
r = rate,
t = time

ProblemSolving Strategy—Distance, Rate, and Time Applications

Read the problem. Make sure all the words and ideas are understood.
Draw a diagram to illustrate what it happening.
Create a table to organize the information: Label the columns rate, time, distance. List the two scenarios. Write in the information you know.

Identify what we are looking for.

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.
Multiply the rate times the time to get the distance.

Translate into an equation.
Restate the problem in one sentence with all the important information.
Then, translate the sentence into an equation.

Solve the equation using good algebra techniques.

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

Answer the question with a complete sentence.
Practice makes perfect
Solve Uniform Motion Applications
In the following exercises, solve.
Lilah is moving from Portland to Seattle. It takes her three hours to go by train. Mason leaves the train station in Portland and drives to the train station in Seattle with all Lilah’s boxes in his car. It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train. Find Mason’s speed and the speed of the train.
Mason 75 mph, train 60 mph
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Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in 4.8 hours and Cheryl completes the course in 8 hours. Kathy walks two miles per hour faster than Cheryl. Find Kathy’s speed and Cheryl’s speed.
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Two busses go from Sacramento for San Diego. The express bus makes the trip in 6.8 hours and the local bus takes 10.2 hours for the trip. The speed of the express bus is 25 mph faster than the speed of the local bus. Find the speed of both busses.
express bus 75mph, local 50 mph
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A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet 1.1 hours for the flight, and it takes the private airplane 1.8 hours. The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane. Find the speed of both airplanes.
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Saul drove his truck 3 hours from Dallas towards Kansas City and stopped at a truck stop to get dinner. At the truck stop he met Erwin, who had driven 4 hours from Kansas City towards Dallas. The distance between Dallas and Kansas City is 542 miles, and Erwin’s speed was eight miles per hour slower than Saul’s speed. Find the speed of the two truckers.
Saul 82 mph, Erwin 74 mph
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Questions & Answers
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
definition of quadratic formula
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 w2.6=7.55
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?
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?
$1.38 worth of strawberries + $1.14 worth of blueberries which= $2.52
Leitha
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
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
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/(x25) = 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?
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?
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?
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?
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÷48
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
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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