Jamal’s trip requires him to drive 20 mi to the airport, fly 2,300 mi, and then take a bus 6 mi to his hotel. His average speed driving to the airport is 40 mph, the average speed of an airplane is 575 mph, and the average speed of his bus is 15 mph.
Aside from time waiting for the plane or bus, how long is Jamal in transit?
Bear’s Strategy: | Lion’s Strategy: |
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$$\displaystyle \mbox{Drive Time} = \mbox{20 miles} \times \frac{\mbox{1 hour}}{\mbox{40 miles}} = \mbox{0.5 hours}$$ $$\displaystyle \mbox{Fly Time} = \mbox{2300 miles} \times \frac{\mbox{1 hour}}{\mbox{575 miles}} = \mbox{4 hours}$$ $$\displaystyle \mbox{Bus Time} = \mbox{6 miles} \times \frac{\mbox{1 hour}}{\mbox{15 miles}} = \mbox{0.4 hours}$$ In Transit Time = Drive Time + Fly Time + Bus Time 0.5 + 4 + 0.4 = 4.9 hours |
In Transit Time = Drive Time + Fly Time + Bus Time $$\displaystyle \mbox{Drive Time} = \mbox{20 miles} \times \frac{\mbox{1 hour}}{\mbox{40 miles}} = \mbox{0.5 hours}$$ $$\displaystyle \mbox{Fly Time} = \mbox{2300 miles} \times \frac{\mbox{1 hour}}{\mbox{575 miles}} = \mbox{4 hours}$$ $$\displaystyle \mbox{Bus Time} = \mbox{6 miles} \times \frac{\mbox{1 hour}}{\mbox{15 miles}} = \mbox{0.4 hours}$$ 0.5 + 4 + 0.4 = 4.9 hours |
1 Whose Strategy was Top Down? How do you know?
2 Whose Strategy was Bottom Up? How do you know?
3 Which way of thinking about the problem makes more sense to you?
What’s happening with that Math?!
When calculating Jamal’s drive time, we multiplied distance by speed. More specifically, we multiplied the starting value (20 miles) by $$\displaystyle \frac{\mbox{1 hour}}{\mbox{40 miles}}$$. Why? Why not reverse it, to use $$\displaystyle \frac{\mbox{40 miles}}{\mbox{1 hour}}$$, as stated in the problem?
Time is the desired outcome. Looking at the units, we can see that speed must have miles as its denominator to cancel out the miles in the starting value.
$$\displaystyle \frac{\mbox{20 miles}}{1} \times \frac{\mbox{1 hour}}{\mbox{40 miles}} = \frac{20\require{enclose} \enclose{horizontalstrike}{\mbox{miles}} \times \mbox{1 hour}}{40 \require{enclose} \enclose{horizontalstrike}{\mbox{miles}}} = \frac{20}{40} \mbox{hour} = \frac{1}{2} \mbox{hour}$$
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927).
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