Motion Tables and Work Rates Practice

Identify the method: A cyclist travels 60 km to a park and returns along the same route at a slower speed.

Distance-speed-time table, because there is a physical distance traveled (60 km).

Identify the method: An inlet pipe fills a tank in 4 hours while a drain empties it in 6 hours.

Work rate method (part done in one hour), because an entire task is being completed rather than a distance traveled.

Convert 40 minutes into an hourly value for a distance-speed-time equation.

40/60 = 2/3 of an hour (approx. 0.667 hours). Never write 0.40 hours.

A painter finishes a room in 4 hours. A second painter finishes the same room in 12 hours. What fraction of the room do they finish together in one hour?

1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 of the room per hour.

Using the painter problem above, how many hours does it take both painters working together to finish the entire room?

3 hours (the reciprocal of 1/3).

A delivery van drives 120 km. At a speed of x km/h, write the expression for time. Then write the time expression if speed increases by 10 km/h.

Original time is 120/x. Faster time is 120/(x + 10).

A motorboat goes 30 km downstream in 2 hours and 30 km upstream in 3 hours. Find the boat speed in still water and the current speed.

Downstream speed = 30/2 = 15 km/h (boat + current). Upstream speed = 30/3 = 10 km/h (boat - current). The boat speed is 12.5 km/h and the current speed is 2.5 km/h.