Overtake
Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?
Age
14 to 16
Challenge level
Tom left a motorway service station and travelled towards Glasgow at a steady speed of 60 mph. Tim left the same service station 10 minutes after Tom and travelled in the same direction at a steady speed, overtaking Tom after a further 1 hour 40 minutes.
At what speed did Tim travel?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Answer: 66 mph
| Tom starts | 60 miles per hour | 1 hour 50 minutes = 110 minutes |
|---|---|---|
| Tim starts 10 minutes later | speed unknown | 1 hour 40 minutes = 100 minutes |
Finding the distance
Tom: 60 miles per hour $\Rightarrow$ 110 miles in 110 minutes
Tim travels 110 miles in 100 minutes
11 miles in 10 minutes
66 miles in 1 hour
Using ratio
Both travel the same distance.
Times in ratio 110 : 100
$\therefore$ speeds in ratio 100 : 110 = 10 : 11 = 60 : 66
Using algebra
Say Tim's speed is $v$.
Tom and Tim travel the same distance, so $$\begin{align}
60\times1\frac56 &= v\times 1\frac46\\
\Rightarrow 110&=\frac53v\\
\Rightarrow 22 &= \frac13v\\
\Rightarrow 66 & =v \end{align}$$