Jordan drove to town at 50 mph and rove back home at 40 mph

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?

Solution

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
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since going and coming back equal the same distance, then RT going and RT coming back are equal to each other.
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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
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50 * (4) = 200 miles = D
40 * (5) = 200 miles = D
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numbers check out.
4 hours + 5 hours = 9 hours for the round trip.
distance to town is 200 miles.