A boat travels with a speed of 20 km/h in still water. On a day trip, the boat travels upstream and then makes the return trip downstream. The total distance for the trip is 70 km and the total time is 4 hours 15 min. What is the speed of the water?

This is a distance, speed and time question so we use the equation: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi»speed«/mi»«mo»=«/mo»«mfrac»«mi»distance«/mi»«mi»time«/mi»«/mfrac»«/mstyle»«/math»

The equation can be rewritten as «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi»time«/mi»«mo»=«/mo»«mfrac»«mi»distance«/mi»«mi»speed«/mi»«/mfrac»«/mstyle»«/math» which we need to complete the chart below.

1. State what the variable will represent. Usually this is what the question is asking you to find.

x = the speed of the water.

2. Organize the information in a chart. The columns should be distance, speed and time. The rows should be the two parts of the journey (upstream and down, there and back or return trip, etc.

 Distance  Speed  Time
Part 1
Upstream 		  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn»35«/mn»«/mstyle»«/math»   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn»20«/mn»«mo»-«/mo»«mi»x«/mi»«/mstyle»«/math»
  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»35«/mn»«mrow»«mn»20«/mn»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/mstyle»«/math»
 Part 2
Downstream 		  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn»35«/mn»«/mstyle»«/math»
   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mn»20«/mn»«mo»+«/mo»«mi»x«/mi»«/mstyle»«/math»
   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»35«/mn»«mrow»«mn»20«/mn»«mo»+«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

3. Write an equation. There will be a piece of information in the question that will link the two times together. A difference in the times means that you will subtract, a total time means that you will add.

The total time for the trip is 4 hours and 15 min which is 4.25 hours.

«math style=¨font-family:Arial¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mn»35«/mn»«mrow»«mn»20«/mn»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»35«/mn»«mrow»«mn»20«/mn»«mo»+«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»4«/mn»«mo».«/mo»«mn»25«/mn»«/mstyle»«/math»

4. Solve the equation.

This can be solved algebraically or graphically as shown below.

5. Answer the question.

The speed of the water is 8.4 km/h.