Question

When Mr. Johnson drives from Cambridge to Newton it takes him 15 minutes travelling at a speed of 80 miles per hour. Mrs. Johnson drives from Cambridge to Newton and leaves 10 minutes after Mr. Johnson but travels at a speed of 100 miles per hour. Who will arrive first? By how many minutes?

Answer 1

Given :

Time taken by Mr. Johnson to drive from Cambridge to Newton = 15 mins

Speed of Mr. Johnson = 80 miles per hr

Speed of Mrs. Johnson = 100 miles per hour

To Find :

If Mrs.Johnson leaves 10 mins after Mr. Johnson then who arrives first and by how many minutes ?

Solution :

Since the speed and time taken by Mr. Johnson is given , so we can find the distance between Cambridge and Newton as :

$speed = \frac{distance}{time }$

So, $80 \frac{miles }{hr} = \frac{d}{\frac{15}{60}hr}$

Or, d = $80 \times \frac{15}{60 }$

Or, d = 20 miles

Now the time taken by Mrs Johnson to cover this 20 miles at a speed of 100 miles per hr will be :

t = $\frac{distance}{speed }$

Or, t = $\frac{20}{100}$

Or, t = $\frac{1}{5}$ hour

Or , t = $\frac{1}{5}\times 60 mins$

So , t = 12 mins

Now since Mrs Johnson takes only 12 mins but she left house 10 mins after Mr Johnson who takes 15 mins .

So in reference to the time at which Mr Johnson leaves the time taken by Mrs Johnson is = 12 + 10 = 22 mins

Hence , Mr Johnson arrive first and he arrives 7 mins earlier than her .