Question

Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school

Answer 1

Her usual time from home to school is 30 minutes

Explanation:

At any point in time;

distance = speed * time

Here, we want to calculate the normal time she spent going from home to school

Let the normal time be x minutes

And the normal speed be t m/min

Today, she increased her speed by 20%

Her speed today will be t + 20/100 * t =

1.2t m/min

Her distance from how to school normally is

xt meters

Now what this means is that, at the increased speed, she was able to get to school 5 minutes earlier

What we are saying is although, she lost 20 minutes initially, she was able to beat down the lateness by 5 minutes

So, the time spent on her increased speed journey is;

(x-5) minutes

At any point in time, the distance will be equal;

Thus, mathematically;

xt = 1.2t(x-5)

xt = 1.2xt - 6t

6t = 1.2xt-xt

6t = 0.2xt

t cancels out

0.2x = 6

x = 6/0.2

x = 30 minutes