SOLUTION: PLEASE HELP ME WITH THE ANSWER TO THIS WORD PROBLEM: Jordan drove to town at 50 mph and rove back home at 40 mph. What is the distance to town if the whole trip took 9 hours?

Question 207109This question is from textbook Algeba I: An Incremental Development
: PLEASE HELP ME WITH THE ANSWER TO THIS WORD PROBLEM:
Jordan drove to town at 50 mph and rove back home at 40 mph. What is the distance to town if the whole trip took 9 hours?
THANK YOU SO SO SO MUCH :) This question is from textbook Algeba I: An Incremental Development

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
going = 50 mph.
coming back = 40 mph.
total time = 9 hours
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RT=D
R = rate = miles per hour.
T = time = hours.
D = distance = miles.
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let x = time it took to go
let y = time it took to come back
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50*x = D
40*y = D
x + y = T
-----
since going and coming back equal the same distance, then RT going and RT coming back are equal to each other.
-----
50*x = 40*y
x = 40*y/50
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equation of x + y = T becomes:
40*y/50 + y = T which becomes:
multiply both sides of this equation by 50 to get:
40*y + 50*y = 50*T which becomes:
y*(40+50) = 50*T which becomes:
90*y = 50*T
divide both sides of this equation by 90 to get:
y = (50/90)*T which becomes:
y = (5/9)*9 = 5
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y = 5 hours means that x must = 4 hours because x + y = 9
-----
50 * (4) = 200 miles = D
40 * (5) = 200 miles = D
-----
numbers check out.
4 hours + 5 hours = 9 hours for the round trip.
distance to town is 200 miles.
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