Linear Worded Equation

Question

A group of hikers is to travel x km by bus at an average speed of 48km/h to an unknown destination. They then plan to walk back along the same route at an average speed of 4.8 km/h and to arrive back 24 hours after setting out in the bus. If they allow 2 hours for lunch and rest, how far must the bus take them?

Answer 1

Note that, given the 2 hours for rest and meal, the actual total travelling time

is 22 hours.

 

Distance = rate*time

Let d = distance one way

Bus: d = 48t

Walk: d = 4.8(22-t)

 

Since they travel the same distance both ways:

48t = 4.8(22-t)

48t = 105.6 - 4.8t

52.8t = 105.6

t = 2

 

d = 48t = 48(2) = 96 km