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Example 3.51 from Elementary Algebra, 3.5 Solve Uniform Motion Applications
Solve Uniform Motion Applications: example 3.51
When Katie Mae walks to school, it takes her 30 minutes. If she rides her bike, it takes her 15 minutes. Her speed is three miles per hour faster when she rides her bike than when she walks. What are her walking speed and her speed riding her bike?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
First, we draw a diagram that represents the situation to help us see what is happening.
We are asked to find her speed walking and riding her bike. Let’s call her walking speed r. Since her biking speed is three miles per hour faster, we will call that speed We write the speeds in the chart.
The speed is in miles per hour, so we need to express the times in hours, too, in order for the units to be the same. Remember, one hour is 60 minutes. So:
Next, we multiply rate times time to fill in the distance column.
The equation will come from the fact that the distance from Katie Mae’s home to her school is the same whether she is walking or riding her bike.
So we say:
Translate into an equation. Solve this equation. Clear the fractions by multiplying by the LCD of all the fractions in the equation. Simplify.
6 mph
(Katie Mae's biking speed)Let's check if this works.
Walk 3 mph (0.5 hour) = 1.5 miles
Bike 6 mph (0.25 hour) = 1.5 milesYes, either way Katie Mae travels 1.5 miles to school. Katie Mae’s walking speed is 3 mph.
Her speed riding her bike is 6 mph.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower. It takes her 30 minutes to hike back down to the parking lot. Her speed going downhill is 1.2 miles per hour faster than her speed going uphill. Find Suzy’s uphill and downhill speeds.
How did it go?