"I was walking along the road at 3 1/2 miles/hour," said Bill, "when the car dashed past me, missing me by a few inches."
"Do you know at what speed it was going? asked the policeman.
"Well, from the moment it passed me to its disappearance round the corner I took 27 steps and walking on reached the corner with 135 steps more."
"Then, assuming that you walked, and the car ran, each at a uniform rate, I can easily work out the speed," said the policeman.
Hint: Do you need to know the size of Bill's step?
Do you need to use the famous d=rt formula?
Is there a way to think through the problem to a solution, without alot of computational work or conversion of units?
Solution Commentary: Draw a diagram. Once the car passed Bill, he needed 27 steps to see the car reach the corner and then another 135 steps to reach the corner himself. From when the car passsed him, Bill traveled a total of 162 steps. Now, the car did these same 162 steps in the same amount of time that it took for Bill to do 27 steps.
Thus, the car is travelling how many times faster than Bill? (6)
The car's rate is what? (21 mph)
Students often have trouble with this problem because they cannot conceive a car "dashing by" at the rate of 21 mph....then I tell them that I took this out of a mathematics text in the early 1920's.