SOLUTION: A lady traveled 100 kilometers at a rate of 30 kilometers an hour. If she wants her return trip to be three-fourths of her trip, at what rate must she return?

Question 1166743: A lady traveled 100 kilometers at a rate of 30 kilometers an hour. If she wants her return trip to be three-fourths of her trip, at what rate must she return?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
r*t=d
r = rate
t = time
d = distance

the lady traveled 100 kilometers at a rate of 30 kilometers per hour.
the formula for her becomes 30 * t = 100
solve for t to get t = 100 / 30 = 10/3 hours.

she wants her return trip to take 3/4 of the time it took her to get to her destination.

3/4 * t = 3/4 * 10/3 = 30/12 = 10/4.

instead of taking 10/3 hours, the trip back should take 10/4 hours.

the formula of r * t = d becomes:
r * 10/4 = 100
solve for r to get:
r = 400/10 = 40

going there she travels at 30 kilometers per hour.
coming back she travels at 40 kilometers per hour.

the formula for going there is 30 * t = 100
the formula for coming back is 40 * t = 100

the time for going there is 100 / 30 hours.
the time for coming back is 100 / 40 hours.

3/4 * 100 / 30 is equal to 300 / 120 which is equal to 100 / 40.
that's the time it takes to get back, confirming the solution is correct.

the solution is that she must comes back at the rate of 40 kilometers per hour.

i worked in fractions because the decimals were repeating.
you can work in decimals as well as long as you round to enough decimal digits so that the repeating decimals will still give you the correct answer.

for example, i did the following:

r * t = d becomes 30 * t = 100 when she is going to her destination.
solve for t to get t = 100/30 = 3.33333 rounded to 5 decimal places.
she wants t on the return trip to be equal to 3/4 of the time going.
3/4 * t = 3/4 * 3.33333 = 2.5
the formula of r * t on the return trip becomes r * 2.5 = 100
solve for r to get r = 100 / 2.5 = 40 hours.

working in decimal wasn't as bad as i thought.
either way, you get the same answer.
the answer is 40 kilometers per hour.

your solution is that she would have to travel back at 40 kilometers per hour so that the time required on the return trip is 3/4 of the time taken getting to her destination.

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