Question

Hi! Can anyone help me with this questions? Please and Thank you!

1. If Mr. Cruz will increase his usual rate by 10 kilometers per hour, it will take him one hour shorter to cover a distance of 200 kilometers. What is his usual speed in driving?
2. If you can row upstream to a landing 5 kilometers away and then row back to your starting point all in three hours and 20 minutes and if the river has an average current of 2 kilometers per hour, at what rate are you able to row in still water?

Answer 1

for problem (1)
let u=initial speed in km/h, t=required time to cover the distance with speed u in h
so without increment of speed,
ut=200 ............................(a)
with increment of speed,
(u+10)(t-1)=200.
=> (u+10)(200/u-1)=200 [from (a) t=200/u]
=> 200-u+2000/u-10=200
=> u-2000/u+10=0
=>u^2+10u-2000=0
=> (u+50)(u-40)=0
so u=-50 or 40
physically acceptable solution is u=40 km/h

Answer 2

for problem (2)
let u=speed in the still water in km/h, t=time required to cover 5 km in upstream in h,
then,
(u+2)t+(u-2)(10/3-t)=5+5 [total time=3h 20 min=3(20/60)h=3(1/3)h=10/3h]
=>ut+2t+10u/3-ut-20/3+2t=10
=> 10u+12t-20=30
=> 10u+12t=50
=> u+1.2t=5
=> t=(5-u)/1.2 ...................................(a)

now (u+2)t=5
=> (u+2)(5-u)/1.2=5 [putting value of t from (a)]
=>10+3u-u^2=6
=> u^2-3u-4=0
=> (u-4)(u+1)=0
so u=4 or -1
acceptable solution u=4km/h.

Answer 3

Thank you! It is much appreciated..