on the way there 56 mph way back 70 mph. Time it took 4.5 hrs. How long did it take to get back to were I started

Question

This is a little math problem I've been stuck on for a while.

Answer 1

Do you mean that the round trip took 4.5 hours?

 

In that case, we can solve the problem as follows:

 

Distance = (Rate)(Time)

 

Let x = time it takes on the way back

 

Then, 4.5 - x = time on the way there

 

Since the distances each way are equal, we have:

 

56(4.5 - x) = 70x

 

So, 252 - 56x = 70x

 

             252 = 126x

 

                x = 2 hours

 

 

Answer 2

Hi Nicholas, if I understand the problem correctly, you made a round trip from point a to point b and back to point a. This problem is an application of the time, rate of speed, and distance equation, D(istance) = T(ime) X R(ate).

 

You need to use the time, rate of speed, and distance equation twice. The first time, you determine the distance from point a to point b because you are given the time (4.5 hours) and the rate of speed (56 mph) it took to get from point a to point b.

 

The second time, you use the time, rate of speed, and distance equation, you need to solve the equation for T(ime) because you know the distance (calculated from the first step) and the rate of speed(70 mph.)

 

Questions?

 

Answer 3

Remember that Distance = Rate x Time.

 

On the way there, it took 4.5 hours at 56 mph, so the distance of the trip was  56x4.5 = 252 miles

 

The trip back is the same distance, and the speed is known, so we can put those into the formula:

 

    252 = 70 x T

 

Divide both sides by 70, and you'll see that T = 3.6 hours.