Todds average speed when riding his road bike is 4 mph faste

Todd’s average speed when riding his road bike is 4 mph faster than Bill’s average speed. It took Todd one hour less to complete an 80-mile bike ride than it took Bill to complete the same ride. What is Bill’s average speed?

Solution

Todd’s average speed when riding his road bike is 4 mph faster than Bill’s average speed

Let Bill\'s avg speed be x mi/hr

So, Todd\'s avg speed = ( x+4) mi/hr

Time taken by Biil to cover 80 miles = 80/x

Time taken by Todd to cover 80 miles = 80/(x+4)

Time defference = 1hr

80/x - 80/(x+4) -=1

1/(x+4) - 1/x = 1/80

Taking LCD as (x(x+4):

( x- x -4)/x(x+4) = 1/80

4/x(x+4) = 1/80

x^2 +4x - 320 =0

Solve the qadratic equation : we get x= 16 mi/hr ; x= -20mi/hr

neglect -ve value:

So, Bill\'s avg speed = x = 16mi/hr