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 for an half an hour for lunch. To reach City B on time, the motorcyclist increases his speed after lunch by 10 km/hr. Find the original speed of the motorcyclist. Thank you!

Answer 1

Explanation:

Original time to get there = 225/x hours, where x = original speed km/hr

After 1.5 hr , rider has traveled 1.5 x km and has 225 - 1.5x km to go

rider stops for 1/2 hr so rider has used 2 hours

225/x -2 = time left to get there

Now increase the speed by 10

( 225-1.5x ) / ( x+10) must equal the time left to get there

(225- 1.5x) / ( x+10) = 225/x - 2 multiply both sides by x

x ( 225-1.5x) / ( x+10) = 225 - 2x now multiply both sides by (x+10)

x ( 225-1.5x) = (x+10)(225-2x) expand both sides

-1.5x^2 + 225 x = - 2x^2 + 225x + 2250 - 20x simplify

.5x^2 +20x -2250 = 0 Use Quadratic Formula with

a = .5 b = 20 c= - 2250

to find x = original speed = 50 km/hr