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Answer: 66 mph
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 $$\begin{align}
60\times1\frac56 &= v\times 1\frac46\\
\Rightarrow 110&=\frac53v\\
\Rightarrow 22 &= \frac13v\\
\Rightarrow 66 & =v \end{align}$$
Overtake
Age 14 to 16
ShortChallenge Level 
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 $$\begin{align}
60\times1\frac56 &= v\times 1\frac46\\
\Rightarrow 110&=\frac53v\\
\Rightarrow 22 &= \frac13v\\
\Rightarrow 66 & =v \end{align}$$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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