A couple of friends decide to race each other. Clare can run 8 yards per second, whereas Gabby can run 9 yards per second. Because she is slower, Clare also gets a head start of 10 yards. Shortly after they start running, Gabby will catch up to Clare. How far will Gabby have to run? How long will that take?
Question
A couple of friends decide to race each other. Clare can run 8 yards per second, whereas Gabby can run 9 yards per second. Because she is slower, Clare also gets a head start of 10 yards. Shortly after they start running, Gabby will catch up to Clare. How far will Gabby have to run? How long will that take?
Solution
To solve this problem, we first need to understand that Gabby is running 1 yard per second faster than Clare. This means that for every second that passes, Gabby closes the distance between them by 1 yard.
Since Clare has a head start of 10 yards, it will take Gabby 10 seconds to close this gap (because she's running 1 yard per second faster).
The distance Gabby will have to run is her speed multiplied by the time. So, Gabby runs at 9 yards per second for 10 seconds, which equals 90 yards.
So, Gabby will have to run 90 yards to catch up to Clare, and it will take her 10 seconds to do so.
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