SOLUTION: 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 th

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?
Answer by yuvaraja(2) (Show Source): You can put this solution on YOUR website!
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.

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