In 14 of an hour more time Jack riding a bicycle at 12 mph

In 1/4 of an hour more time ,Jack , riding a bicycle at 12 mph, rode 6 mies farther than Tom, who was riding his bycycle at 10 mph. How long did Jack ride?

Solution

In 1/4 of an hour more time ,Jack , riding a bicycle at 12 mph, rode 6 mies farther than Tom, who was riding his bycycle at 10 mph. How long did Jack ride?
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J = the distance Jack rode
M = the distance Tom rode (T might be confused with t for time)
t = the time Tom rode
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distance = rate x time
J = 12*(t + 1/4) (Jack rode 1/4 hr longer than Tom)
M = 10t
J = M + 6 (Jack rode 6 miles farther)
Sub for M
J = 10t + 6
J = 12*(t + 1/4) 1st eqn
10t + 6 = 12*(t + 1/4)
10t + 6 = 12t + 3
2t = 3
t = 1.5 hours
Jack rode 1/4 hour longer, = 1.75 hours or 1 hour 45 minutes.