+389 Janene and Emily plan to go on a marathon training run. Emily arrives late, so Janene starts running 16 minutes before Emily. Janene runs at an average rate of 9 minutes per mile, and Emily runs at an average rate of 8 1/4 minutes per mile. Assuming that both girls started at the same location and ran the same route, how many minutes will Emily take to catch up to Janene?
+128456 If Janene runs 1 mile in 9 minutes, each minute, she runs (1/9) of a mile.
And if Emiliy runs 1 mile in 8.25 minutes, then each minute she runs (1/8.25) = (4/33) of a mile
Then, in each minute, the amount of ground that Emily "makes up" on Janene = (4/33) - (1/9) = 1/99 mi
And, if Janene runs for 16 minutes before Emily arrives, she is 16(1/9) = 16/9 miles ahead of Emily when Emily starts.
So.....the time it will take Emily to catch Janene is given by (1/99)M = 16/9 where M is the time in minutes.
Multiply both sides by 99 and we have M = (99/9)*16 = 11 * 16 = 176 minutes for Emily to catch Janene
+128456 If Janene runs 1 mile in 9 minutes, each minute, she runs (1/9) of a mile.
And if Emiliy runs 1 mile in 8.25 minutes, then each minute she runs (1/8.25) = (4/33) of a mile
Then, in each minute, the amount of ground that Emily "makes up" on Janene = (4/33) - (1/9) = 1/99 mi
And, if Janene runs for 16 minutes before Emily arrives, she is 16(1/9) = 16/9 miles ahead of Emily when Emily starts.
So.....the time it will take Emily to catch Janene is given by (1/99)M = 16/9 where M is the time in minutes.
Multiply both sides by 99 and we have M = (99/9)*16 = 11 * 16 = 176 minutes for Emily to catch Janene
