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# Hard algebra question

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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JohnMac328
2 Solutions

Commented:
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 Commented:
I am having trouble with part C, what equation can I use to solve this part?
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Commented:
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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PrincipalCommented:
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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Commented:
I think you mean mph  not mpg  ;)
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Author Commented:
Thanks!
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