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# Algebra

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For travel from Washington DC to Baltimore by car, a constant speed of 60 mph was maintained. For the return trip, there was a constant speed \(80\) mph. What was the average speed over the whole two-way trip?

Apr 16, 2022

#1
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Because it's the same distance, it is \((60 + 80) \div 2 = \color{brown}\boxed{70} \) mph.

Apr 16, 2022
edited by BuilderBoi  Apr 16, 2022
#2
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The time at 60 mph    d/60

The time at 80 mph    d/80

Time for the whole trip     2d / a          where a = average

d/60 + d/80 = 2d/a

a = 2d / ( d/60 + d/80) = 2 / ( 1/60 + 1/80) = 2 / ( 7/240) = 68.57 mph average

Apr 16, 2022
#3
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Gahh... Speed is tricky

BuilderBoi  Apr 16, 2022
#4
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At first blush, we might assume that the avg speed  =  70  mph

However, the avg speed will actually be slower

Here's an easy formula  to  figure average speed when the distances are the same  going  and returning

Avg speed =    2 (product of the  rates)  /(sum of the rates)   =

2 (60 *80)  /( 60 + 80)  =

9600  / 140    ≈  68.57 mph   Apr 17, 2022