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| Math Central | Quandaries & Queries |
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Question from Tea, a student: Serena and Nina are taking a train from Vancouver to Whistler, a 160km trip. If the average speed is decreased by 16km/hr, the trip will be 1/2 hours longer. What is the average speed of the train? |
Hi Tea,
The key to this problem is that average speed is distance over time. Suppose that the average speed of the train is $s$ km/hr and the trip from Vancouver to Whistler at this speed takes $t$ hours. Then, since speed is distance divided by time,
\[s = \frac{160}{t} \mbox{ kilometers per hour.}\]
Suppose now that the average speed of the train decreases by 16 km/hr. What is the new average speed? At this speed the train takes 1/2 hour longer so at this speed how long will the trip take? For this trip write an equation for the average speed is distance over time. You now have two equations in $s$ and $t,$ Solve for $s.$
Write back if you need more assistance,
Penny
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