Joan left Durham traveling 85 mph. Mike,to catch up,left some time later driving at 94 mph. Mike caught up after 7 hours. How long was Joan driving before Mike caught up?

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Joan left Durham traveling 85 mph. Mike,to catch up,left some time later driving at 94 mph. Mike caught up after 7 hours. How long was Joan driving before Mike caught up?

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Answer 1 · 2018-04-26T13:05:46

Joan had been driving for $7$ $7$ hours $44$ $44$ mins

Explanation:

*Before we start we should immediately note that $speed, distance and time$ $"speed, distance and time"$ are all present in the question. Therefore we know we will most likely need to use the equation: $Speed = \frac{Distance}{Time}$ $"Speed"="Distance"/"Time"$

Firstly let's call the place where the two people meet $x$ $x$ .

To get to point $x$ $x$ Joan travelled at $85 m p h$ $85mph$ for $y$ $y$ amount of time.

To get to point $x$ $x$ Mike travelled at $94 m p h$ $94mph$ for $7$ $7$ hours.

Mike has given us both $speed and time$ $"speed and time"$ We can, therefore, now work out the distance Mike meets Joan.
-Rearrange the formula : $Distance = Speed \times Time$ $"Distance"="Speed" times "Time"$

$Distance = 94 \times 7$ $"Distance"=94 times 7$

$Distance = 658 miles$ $"Distance"=658"miles"$

We now know that the point they both meet at (which we called $x$ $x$ to start with is: $658$ $658$

We now know the $Distance and Speed$ $"Distance and Speed"$ of Joan. We can, therefore, work out the length of time Joan has been travelling.
-Rearrange the formula: $Time = \frac{Distance}{Speed}$ $"Time"="Distance"/"Speed"$
$Time = \frac{658}{85}$ $"Time"=658/85$

$Time = 7.74 hours (2 . D . P .)$ $"Time"=7.74"hours"(2.D.P.)$

Now all that remains for us to do is work out how many minutes Joan has been travelling for.

$\frac{mins}{60} \times 100 = 74$ $"mins"/60 times 100=74$

$\frac{mins}{60} = \frac{74}{100}$ $"mins"/60=74/100$

$mins = \frac{74}{100} \times 60$ $"mins"=74/100 times 60$

$mins = 44$ $"mins"=44$

Joan has therefore been travelling for $7$ $7$ hours $44$ $44$ mins

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Joan left Durham traveling 85 mph. Mike,to catch up,left some time later driving at 94 mph. Mike caught up after 7 hours. How long was Joan driving before Mike caught up?

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