alanforde800Maximus wrote:A canoeist spent two days on a large lake. On the second day, the canoeist rowed 2 hours longer and at an average speed 2 miles per hour faster than he rowed on the first day. If the canoeist traveled a total of 50 miles and spent a total of 12 hours rowing on his trip, what was his average speed on the first day?
a) 2mph
b) 3mph
c) 4mph
d) 5mph
e) 6mph
Let t = the time on the first day.
Since the time on the second day is 2 hours longer, the time on the second day = t+2.
Since the total time over the 2 days is 12 hours, we get:
t + (t+2) = 12
2t = 10
t = 5.
Thus, the time on the first day = 5 hours, while the time on the second day = 7 hours.
Let r = the rate on the first day.
Since the rate on the second day is 2 hours longer, the rate on the second day = r+2.
Thus:
Distance traveled on the first day = (rate on the first day)(time on the first day) = (r)(5) = 5r.
Distance traveled on the second day = (rate on the second day)(time on the second day) = (r+2)(7) = 7r + 14.
Since the total distance traveled over the 2 days is 50 miles, we get:
5r + (7r+14) = 50
12r = 36
r = 3.
The correct answer is
B.
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