Answer:
The difference of the time taken for each of the two journeys is given as follows;
The difference of time = 2000/(x·(x + 10))
Step-by-step explanation:
The speed with which the car completes the 200 km journey = x km/h
The speed with which the car completes the return journey = (x + 10) km/h
Let t₁ represent the time it takes the car to complete the 200 km and let t₂ represent the time it takes the car to complete the return journey, we have;
t₁ = 200/(x)
t₂ = 200/(x + 10)
The difference of the time taken for each of the two journeys = t₁ - t₂
We have;
t₁ - t₂ = 200/(x) - 200/(x + 10)
200/(x) - 200/(x + 10) = (200·(x + 10) - 200·x)/((x)·(x + 10)) = 2000/((x)·(x + 10))
∴ t₁ - t₂ = 2000/((x)·(x + 10)) = 2000/(x·(x + 10))
The difference of the time taken for each of the two journeys = t₁ - t₂ = 2000/(x·(x + 10))
