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36 votes
Suppose you need average speed of 100 km/h to arrive at a certain destination on time. However, trafficlimits your average speed to only 60 km/h during the first half of the trip's distance. What must youraverage speed be in the second half of the trip to be on time?

User Wakjah
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1 Answer

16 votes
16 votes

Answer:

140 km/h

Step-by-step explanation:

If you have a speed of v1 the first half of the trip and a speed of v2, the second half of the speed, the average speed will be


v_{\text{avg}}=(v_1+v_2)/(2)

Solving for v2, we get:


\begin{gathered} 2v_{\text{avg}}=v_1+v_2 \\ 2v_{\text{avg}}-v_1=v_2 \\ v_2=2v_{\text{avg}}-v_1 \end{gathered}

Then, we can replace the average speed Vavg = 100 km/h and the speed of the first half v by 60 km/h


\begin{gathered} v_2=2(100\operatorname{km}/h)-60\operatorname{km}/h \\ v_2=200\operatorname{km}/h-60\operatorname{km}/h \\ v_2=140\operatorname{km}/h \end{gathered}

Therefore, the speed in the second half of the trip must be 140 km/h

User ToddSmithSalter
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