Question

A motorcyclist leaves City A and rides at a constant speed towards City B, which is 225 km away. After 1.5 hours, the motorcyclist stops a half an hour lunch. To reach City B on time, the motorcyclist increases his speed after lunch by 10km/hour. Find the motorcyclists original speed

Answer 1

50 km/hr

Explanation:

OK, this is how I solved this problem.

Let r = original rate of speed

t = time after the stop to finish the trip

Time for trip without stopping is 225/r

(1) 1.5 + .5 + t = 225/r This is a time equation

(2) 1.5r + t(r + 10) = 225 This is a distance equation

(1) 2 + t = 225/r (2) 1.5r + tr + 10t = 225

2r + tr = 225

tr = 225 - 2r 1.5r + 225 - 2r + 10(225/r - 2) = 225

t = 225/r - 2

-.5r + 225 + 2250/r - 20 = 225

-5r + 2250 + 22500/r - 200 = 2250

-5r^2 + 2250r + 22500 - 200r = 2250r

5r^2 + 200r - 22500 = 0

5(r^ + 40r - 4500) = 0

5(r - 50)(r + 90) = 0

r = 50 or r = -90

The rate cannot be negative, so the original speed 50 km/hr

This not an easy problem and I hope you were able to follow my work