Thought 21: Maths with Calvin

Foreword

The following maths problem 

is taken from the comic book

series Calvin and Hobbes.

Problem

Mr Jones lives 50 miles away from you. 

You both leave home at 5.00 and drive toward each other. 

Mr Jones travels at 35 mph, and you drive at 40 mph. 

At what time will you pass Mr Jones on the road?

Method

I actually solved this one using a diagram.

In any event, this is how it can be reduced to, 

having no great formal education in mathematics. 

Mr Jones travels at 35 miles per hour, 
which is to say 35 miles per sixty minutes. 

I divided time by distance, 

namely sixty minutes by thirty five miles,

to find out the time needed to cover 

one mile at that speed. 

Result: 1.7 minutes. 

So ten miles travelling at the speed 

of 35 miles per hour 

takes 17 minutes 

(1.7 x 10). 

Since the overall distance between 

Mr Jones' place and yours is fifty miles, 

that distance can be covered in 

17 minutes (for the ten miles)

 multiplied by 5 (to make fifty miles) 

which gives 85 minutes.

Meanwhile, you travel at 40 miles per hour, 
which is to say, you cover 40 miles 
per every sixty minutes. 

Same method as above: 

60 divided by 40 gives 

the time needed to cover 

one mile travelling at that speed. 

Result: 1.5 minutes. 

So ten miles travelling at 40 mph

 is equivalent to 1.5 x 10 = 15 minutes. 

So, for fifty miles,

we need to multiply

the 15 minutes it takes

to travel ten miles

by five. 

15 x 5 = 75 

75 minutes 

is required when travelling 

at the speed of forty miles per hour

to cover fifty miles of road.

To find out the time at which Mr Jones 
and yourself cross each other, 
one needs to subtract 
75 minutes from 85 minutes 
which gives ten minutes. Why? 
Because this difference will yield 
the exact time needed 
for the two cars to pass. 
Result: ten minutes.

Solution

Since both you and Mr Jones leave home at 5.00 pm, 
and that it takes ten minutes for the cars to pass
each other travelling at their respective speeds,
you will pass each other at exactly 5.10 pm.

There you go Calvin!