Question

You went to Disney World by car. The trip there took 6 hours. On the way home, people were evacuating for a possible hurricane so your speed decreased by 20 m/hr and it took 10 hours to get home. How fast was the car going on the way there? How fast was it going on the way back home?

Answer 1

a) on the way there, the speed = 50 m/hr

b) on the way back home, speed = 30 m/hr

Explanation:

`speed (s) = (distance(d))/(time(t)) \\distance = speed\ *\ time`

on the way to Disney land:

distance = d

speed = s

time = t = 6 hours

d = s × t

d = s × 6

d = 6s - - - - - (1)

On the way back:

speed decreased by 20m/hr

This means that s₂ = (s - 20)m/hr

time = t₂ = 10 hours

∴ d = s₂ × t₂

d = (s - 20) × 10

d = 10s - 200 - - - - (2)

Note that the distance is the same to and from disney land, therefore, equation (1) equals equation (2)

∴ 6s = 10s - 200

collecting like terms:

10s - 6s = 200

4s = 200

∴ s = 200 ÷ 4

s = 50 m/hr

Therefore on the way there, the car was moving at a apeed of 50m/hr

speed on the way back home (s₂) = (s - 20) m/hr

∴ s₂ = 50 - 20

s₂ = 30 m/hr

Therefore on the way back home the speed was 30 m/hr