Chris is travelling by boat up the river and it took him 3h to cover 48 km against the current. It then took him 2h for the return trip with the current. What is the speed of the boat in still water and the speed of the current? [K//U 1 marks, App. 3 marks and Comm. 1 mark] plz show all your work and explain it so i understand.
2006-09-17 15:01:51 · 4 answers · asked by MuchCount 1 in Science & Mathematics ➔ Mathematics
It's easy for people with Calculus III and up experience to over analysis these problems...
But I think this is the most "plug and chug" way to answer many similar questions...
First Remember: D=R*T => Distance = Rate*Time
(the word "dirt" is how i remember it)
Let's break it down: D = R * T
Plug the "knowns" into the equation:
--Boat against current: 48 km = R * 3 h
=> R = 16 km/h
--Boat w/current: 48 = R * 2
=> R=24 km/h
Now we solve two equations for two unkowns:
Br = Boat Rate Cr = Current Rate
Boat against current : Br - Cr = 16
Boat with current: Br +Cr = 24
Use substitution to solve for each:
Br = 16 + Cr => 16 + Cr + Cr = 24
= 2Cr = 24 - 16
= Cr = 8/2 = 4 Ans for Current rate
Use Cr = 4 in any of the two equations:
Br - 4 = 16
=> Br = 20 Ans for Boat Rate with out current (still water)
Remember! D = R * T
2006-09-17 15:46:53 · answer #1 · answered by rocketscienceisez 2 · 0⤊ 0⤋
Well, I figure the speed of the boat minus the speed of the current would result in the speed of the boat going upriver, which was 16 km/hr. Boat speed plus current speed is the speed going downriver, 24 km/hr. With a velocity difference of 8 km/hr. The speed of the boat in still water would be midway between the 16 and the 24 because you have an added vector in one case and a subtracted vector (same magnitude) in the other. 8 km/hr divided by two is 4 km/hr (CURRENT SPEED). The midway of the different velocities, 20 km/hr, would be the BOAT SPEED.
2006-09-17 22:21:36 · answer #2 · answered by Adashi 3 · 0⤊ 0⤋
Dewd..... You is in a World of conceptual sh|t.
Going upstream it took him 3 hours to cover 48 km. His speed was 16 km/hr
Coming downstream, it took him 2 hours to cover the same 48 km so his speed was 24 km/hr
The speed of the current and the boat are presumed to have been the same.
Boat speed = B, current speed = C then
B - C = 16
B + C = 48
Solve for B and C.
Doug
2006-09-17 22:17:32 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋
Ok here we go- distance up = distance down
let v = his speed in still water and s be speed of current
since distance = rate x time
rate up = (v-s) (v-s)*3=48
rate down = (v+s) (v+s)*2=48
3v-3s=48
2v+2s=48 solve this system s=4 and v=20 Q.E.D.
2006-09-17 22:41:39 · answer #4 · answered by rwbblb46 4 · 0⤊ 0⤋