   SEARCH HOME Math Central Quandaries & Queries  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.

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