Lesson 25, 2nd Level. Word problems that lead to
Example 3. First, let us explain the meaning of "upstream" and "downstream." When a boat travels in the same direction as the current, we say that it is traveling Thus if Downstream speed = When a boat travels against the current, it travels In this case, its total speed is Upstream speed =
Problem. The speed of a boat in still water is 30 mph. It takes the
Time upstream = Time downstream Now, speed, or
Therefore,
The equation will be
Problem 5. The speed of a boat in still water is 15 mi/hr. If the boat travels 8 miles downstream in the same time it takes to travel 4 miles upstream, what is the speed of the current? To see the equation, pass your mouse over the colored area.
Problem 6. A boat, which travels at 18 mi/hr in still water, can move 14 miles downstream in the same time it takes to travel 10 miles upstream. Find the speed of the current.
Problem 7. Train A has a speed 15 mi/hr greater than train B. If train A travels 150 miles in the
Problem 8. A train travels 30 mi/hr faster than a car. If the train covers 120 miles in the
Example 4. Total time problem. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). She drove back at 75 kph. The total driving time was 7 hours. How far away was Boston?
Time going + Time returning = Total time. Again, time is
Problem 9. You have exactly
Time going + Time returning = Total time.
Example 5. Job problem. Raymond can do a job in 3 hours, while it takes Robert 2 hours. How long will it take them if they work together?
For example, if a job takes 3 hours, then in In general, if a job takes So, let We have,
For in Since
Therefore, on taking reciprocals,
Problem 10. Carlos can do a certain job in three days, while it takes Alec six days. If they work together, how long will it take them? Let
Therefore,
Problem 11. If Jane can do a certain job in 6 hours, but it takes Ana only 4 hours, how long will it take them if they work together?
Problem 12. Two people working together can complete a job in six hours. If one of them works twice as fast as the other, how long would it take the faster one working alone?
Then the other takes
2 Here is the equation:
Problem 13. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. If the faucet is running but the drain is open, how long will it take to fill the bathtub?
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