Question

Meg rowed her boat upstream a distance of 64 miles and then rowed back to the starting point. The total time of her trip was 20 hours. If the rate of the current was 6 mph, find the average speed of the boat relative to the water.

Answer 1

let the speed of the boat in still water = x mph
then speed while going downstream = (x+6) mph
and speed while going upstream = (x - 6) mph
distance = speed x time => time = distance/speed

time1 while going downstream = 64/(x + 6) hr
time2 while going upstream = 64/(x - 6) hr

given that time1 + time2 = 20

=> 64/(x + 6) + 64(x - 6) = 20

Answer 2

We have:

64/(b-6)+64/(b+6)=20 where b is the speed of the boat relative to the water.

So (64(b+6)+64(b-6))/(b+6)(b-6)=20

128b=20(\[b ^{2}-36\])

20b^2-128b-720=0

or

5b^2-32b-180=0

(5b+18)(b-10)=0

We throw out the negative one, giving b=10 mph

You can plug it back in to check.

Answer 3

thank you so much 10 is the answer. :-)

Answer 4

goblue has given the further steps..

however if u want me to complete my solution, let me know...

Answer 5

If you do decide to complete Harikirat, you will need to correct the last line, it appears you exchange your division "/" to a multiplication. "=> 64/(x + 6) + 64(x - 6) = 20"

Answer 6

thanks for pointing out the error :))

Answer 7

I tried it, but got tangled up with the quadratic........I didn't discern the factors lol