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# Hard algebra question

Posted on 2014-02-23
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Elias and Emma are travelling up the San Marcos River in separate canoes. Elias, averaging 3 mph, had gone 5 miles when Emma first put her canoe into the water.
a) How fast must Emma paddle her canoe to catch up to Elias by the end of the 15 mile long canoe route?

b) How long will it take Emma to reach Elias?

c) On the way up the river, the current slowed Elias’ canoe to 3 mph. But on the way back he found that he could paddle 6.5 mph. How fast was the current?

d) How fast could Elias have paddled his canoe if there were no current?
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Question by:JohnMac328

LVL 84

Expert Comment

ID: 39880996
15 miles = t * Emma
15 miles = 5 miles + t * (3 miles / hour)
Emma = 15 miles / ((15 miles - 5 miles)/(3 miles / hour))

3 mph = Elias - current
6.5 mph = Elias + current
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Author Comment

ID: 39881015
I am having trouble with part C, what equation can I use to solve this part?
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LVL 14

Assisted Solution

Don Thomson earned 250 total points
ID: 39881191
Current = C
current Up = -C
Current Down = +C

Speed Down = 3
Speed Up = 6.5

Speed Diff =3.5
Current must be 3.5/2

3+C = 6.5 -C

C=6.5-3 -C

2C=3.5
C=1.75

Nocurrent   = 3 +1.75 or 6.5-1.75

You do the rest
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LVL 25

Accepted Solution

Fred Marshall earned 250 total points
ID: 39881237
a) Elias' speed = 3mph
Elias time at 5 miles = 5/3 = 1.67 hours. (not important here)
Distance remaining for Elias 15-5=10 miles
Time for Elias to complete 10 mi / 3 mph = 3.33 hours.
Time for Emma to complete is the same 3.33 hours.
Emma's speed to complete in 3.33 hours is 15 mi /3.33 hrs = 4.5 mph

b) See the above in (A) 3.33 hours.

c) 3mph = speed over water - current
6.5mph=speed over water + current
subtracting gets 3.5mph = 2*current so current = 3.5/2=1.75mpg

d) speed over ground 3mph
speed over water = 3mph + current = 3 + 1.75 = 4.75 mph
or                           = 6.5mph - current = 6 - 1.75 = 4.75 mph
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LVL 14

Expert Comment

ID: 39882297
I think you mean mph  not mpg  ;)
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Author Closing Comment

ID: 39882693
Thanks!
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