MediumMathematicsHigh School (9–10)GeneralAlgebra › Pairs of Linear EquationsNumericalword problemSAT
A boat takes 5 hours to go 40 km upstream and 4 hours to go the same distance downstream…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A boat takes hours to go km upstream and hours to go the same distance downstream. Find the speed of the boat in still water and the speed of the stream.
Need a reminder? The key ideaShow
Name the two unknowns with their units and write one equation for each fact. A two-digit number with tens digit and units digit is . Downstream speed is and upstream speed is . Check the answer against the words of the problem.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The speeds. Upstream: km/h. Downstream: km/h.
Step 2. The equations. and .
Step 3. Solve. Add: , so . Subtract: , so .
Check. The times are hours and hours.
Answer: the boat goes km/h in still water, and the stream flows at km/h.
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