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S.2 Applications of Simulyaneous Linear Equations

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發問:

A boat travels 60 km upstream in 120 minutes, and returns downstream in 72 minutes. Suppose the speed of the stream is x km/h, and the speed of the boat in still water is y km/h. Find the speed of the stream and that of the boat in still water.

最佳解答:

x + y = (60/72)(60) = 50km/h ----- 1 y - x = (60/120)(60) = 30km/h ----- 2 1 + 2 x+y+y-x = 50 + 30 2y = 80 y = 40 ----- 3 sub 3 into 1 x + 40 = 50 x = 50 - 40 =10 therefore the speed of the stream is 10km/h the speed of boat in still water is 40km/h ----- 驗算 (40-10)km/h in 120minutes = (30km/h)(2h) = 60km (40+10)km/h in 72minutes = (50km/h)(72/60)h = (3600/60) km = 60km

其他解答:

According to yhr question The speed of the boat when travels in the upstream =y-x The speed of the boat when travels in the downstream =y+x So we have 2(y-x)=(72/60)(y+x) [distance=speed*time] 2y-2x=1.2y+1.2x 0.8y=3.2x y=4x Substitute into 2(y-x)=60 x=10 So y=40 the speed of the stream is 10 km/h and that of the boat in still water is 40 km/h
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