Posted by **esther** on Thursday, March 31, 2011 at 9:17pm.

During the first part of a trip a canoeist travels 93 miles at a certain speed. The conoiest travels 5 miles on the second trip at 5mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?

Thank you for all your help.

- algebra 2 -
**Reiny**, Thursday, March 31, 2011 at 9:55pm
speed in first trip ---- x mph

time for 1st trip = 93/x hours

speed in 2nd trip ---- x-5 mph

time for 2nd trip = 5/(x-5)

93/x + 5/(x-5) = 2

93(x-5) + 5x = 2x(x-5)

93x - 465 + 5x = 2x^2 - 10x

2x^2 - 108x + 465 = 0

x = 49.3 or x = 4.7

since the speed in the second trip is reduced by 5, then the new speed would have to be 4.7-5, which is negative. So we'll reject the second answer

check: if speed = 49.3

time = 93/49.3 + 5/44.3 = 1.999 (not bad)

- algebra 2 -
**Esther**, Friday, April 1, 2011 at 12:01am
This answer is wrong, If I can just get the time of the first trip, I can take it from there. I don't need to know the second trip, just the first trip. I appreciate your help. Thank you

- algebra 2 -
**Reiny**, Friday, April 1, 2011 at 8:12am
The answer I gave you is correct for the way the question is given.

The answer was "x=49.3" or the speed on the first part was 49.3 mph and on the second part it was 44.3 mph.

I then checked the answer and got 2 hours as the total time.

The question itself is totally flawed.

I have done enough canoeing in my life time to know that you cannot do a 98 mile canoe trip in 2 hours.

- algebra 2 -
**tchrwill**, Friday, April 1, 2011 at 2:45pm
Reiny is totally correct Ester.

You cannot get the correct speed by considering only the first leg of the trip.

The time of the first leg is T1 = 93/V while the time of the second leg is T2 = 5/(V-5).

Adding, 93/V + 5/(V-5) = 2

Multiplying out and simplifying yields 2V^2 - 108V + 465 = 0 which produces a positive V = 49.282 mph, the speed during the 93 miles trip, the speed during the second leg being 44.282 mph.

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