Question 18817
A troop of scouts hiked to the city at a rate of 2 mph.  they rode back at a rate of 18 mph.  If the round trip took 10 hours, how far is the city?  What is the formula to solve this problem?
Solution:

We have to use the formula,    "Time = Distance/Speed"
(This formula is got from the formula, Distance = Speed * Time)

We know the total time, and rates for the hike and the ride.

Time taken to hike + time taken to rode back = 10 hours ----(1)

Let us take the distance to be x.

Time taken to hike          = Distance / speed = x/2
Time taken to rode back     = Distance / speed = x/18

Plug in these values in (1)

(x/2) + (x/18) = 10.

We have to find the value of x.
Find the common denominator and simplify.
The common denominator is 18.
Multiply the numerator and denominator of the first term by 9.

(9x/18) + (x/18) = 10

Now we have the common denominator. So we can add the numerators.
(9x+x) / 18 = 10.
10x / 18 = 10
Multiply both sides by 18.
10x = 180.
x = 18 miles.