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| Math Central | Quandaries & Queries |
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Question from Ekanem, a teacher: QQ A motorist had planned to reach a place 196km in two hrs exactly. For the first 15km he was able to average only 40km/h. What average speed must he keep up for the rest of the journey if he is to arrive on time. |
Hi Ekanem,
The important fact in this problem is that
\[\mbox{rate} = \frac{\mbox{ distance}}{\mbox{ time}}.\]
First for the entire trip the distance is 196 km and the time is 2 hours so the average rate is
\[\frac{196}{2} = 98 \mbox{ km per hour.}\]
Since he only averages 40 km per hour for the first 15 km he needs to average more than 98 km per hour to make it in 2 hours.
Now let's solve the problem.
For the first 15 km use the fact that
\[\mbox{rate} = \frac{\mbox{ distance}}{\mbox{ time}}\]
to calculate the time it takes. If he is to complete the trip in 2 hours how much time does he have left?
For the second part of the trip use the fact that
\[\mbox{rate} = \frac{\mbox{ distance}}{\mbox{ time}}\]
to calculate the average speed required.
Penny
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