Question

A car travels downhill at 72 mile/hour, on level ground at 63 mile/hour, and uphill at only 56 mile/hour. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hour and 40 mines. Find the distance between the two towns.

Answer 1

let the total distance travelled downhill, on level and uphill be X, Y & Z respectively

time taken to travel a distance at speed v is given as :: t = d/V

The car takes 4 hours to travel from town A to town B.

Time taken for town A to B,

T = X / v₁ + Y / v₂ + Z /v₃

where v₁ = 72 mile/hour

           v₂ = 63 mile/hour

           v₃ = 56 mile/hour

and T = 4 hours

4 = X / 72 + Y / 63 + Z /56    { Equation 1 }

Time taken for town B to A,

T_BA = X / v₁ + Y / v₂ + Z /v₃

where v₁ = 56 mile/hour

           v₂ = 63 mile/hour

           v₃ = 72 mile/hour

and t = 40 hours 40 minutes = 14 / 3 hour

14 / 3 = X / 56 + Y / 63 + 2 /72    { Equation 2 }

simplifying both equation 1 & 2, we get

7X + 8Y + 9Z = 2016                              { equation 3 }

9X + 8Y + 7Z = 2352                      { equation 4 }

adding eq. 1 & eq. 2, we get

16 ( X + Y + Z ) = 4368

X + Y + Z = 4368 / 16 = 273 miles

the total distance between the two towns is 273 miles.