Grade 10 algebra

Question

A cyclist leaves home at 7:30 AM to cycle to school 7 km away. He cycles at 10 km/h until he has a puncture then he has to push his bicycle the rest of the way at 3 km/h. He arrives at school at 8:40 AM. How far did he have to push his bicycle?

Answer 1

Hi Reem,

 

The total time he takes to get to school is 70 mins, or 7/6 hrs. And the distance is 7 km. We are also given the speeds when he rides and pushes the bicycle. So, we have all the information we need. 

Let the time the cyclist pushes the bicycle be x hours.

distance = speed*time

I will use this relationship to solve for x. 

10*((7/6) - x) + 3x = 7  ( i can write this because I know the total time is 7/6 hours)

The rest is solving for x.

70/6 - 10x + 3x = 7

70/6 - 7 = 7x

x = 2/3 hours is the time he pushed the bike.

He did this at a speed of 3 km/h so

d = speed*time 

= (2/3)*3

= 2 km is the distance he pushed the bicycle