Time And Distance Set 7 – Boats
Time And Distance Set 7 – Boats
1. A man can row upstream at 10 km/hr and downstream at 16 km/hr. Find the man’s rate in still water and the rate of current.
A. 13 km/hr, 3 km/hr
B. 10 km/hr, 2 km/hr
C. 3 km/hr, 13 km/hr
D. 15 km/hr, 5 km/hr
Answer
A. 13 km/hr, 3 km/hr
Explanation:
man’s rate in still water = 1/2 (16+10)
man’s rate in still water = 1/2 (16+10)
2. A boat can row at 16 km/hr in still water and the speed of river is 10 km/hr. Find the speed of boat with the river and speed of boat against the river.
A. 13 km/hr, 3 km/hr
B. 15 km/hr, 5 km/hr
C. 26 km/hr, 6 km/hr
D. 6 km/hr, 26 km/hr
Answer
C. 26 km/hr, 6 km/hr
Explanation:
Speed with the river (downstream) = 16+10
Speed against the river (upstream) = 16-10
3. A man goes downstream 60 km and upstream 20 km, taking 4 hrs each. What is the velocity of current?
A. 4 km/hr
B. 8 km/hr
C. 6 km/hr
D. 5 km/hr
Answer
D. 5 km/hr
Explanation:
Downstream speed = 60/4 = 15 km/hr
Upstream speed = 20/4 = 5 km/hr
Velocity of stream = (15-5)/2 = 5 km/hr
4. A man rows downstream 28 km and upstream 16 km, taking 5 hrs each time. What is the velocity of current?
A. 4 km/hr
B. 2.4 km/hr
C. 1.2 km/hr
D. 3 km/hr
Answer
C. 1.2 km/hr
5. A man can row 30 km upstream and 44 km downstream in 10 hrs. Also, he can row 40 km upstream and 55 km downstream in 13 hrs. Find the speed of the man in still water.
A. 5 km/hr
B. 8 km/hr
C. 10 km/hr
D. 12 km/hr
Answer
B. 8 km/hr
Explanation:
Let upstream speed = x, downstream speed = y km/hr
Then, 30/x + 44/y = 10 and 40/x + 55/y = 13
Put 1/x = a, 1/y = b
Solve the equations.
A = 1/5, b = 1/11
So, x = 5, y = 11
Speed in still water = (5+11)/2 = 8
6. A man can row 24 km upstream and 36 km downstream in 6 hrs. Also, he can row 36 km upstream and 24 km downstream in 6.5 hrs. Find the speed of the current.
A. 2 km/hr
B. 8 km/hr
C. 10 km/hr
D. 12 km/hr
Answer
A. 2 km/hr
7. A man can row 6 km/hr in still water. When the river is running at 2 km/hr, it takes him 1 ½ hr to row to a place and come back. How far is the place?
A. 2.5 km
B. 4 km
C. 5 km
D. 10 km
Answer
B. 4 km
Explanation:
B is speed of boat in still water, R is speed of stream
Time is total time taken for upstream and downstream
Distance = time * [B^2 – R^2] / 2*B
=3/2 * [6^2 – 2^2] / 2*6
8. In a stream running at 2 km/hr, a motorboat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed (km/hr) of the motorboat in still water.
A. 17
B. 20
C. 22
D. 25
Answer
C. 22
Explanation:
Distance = time * [B^2 – R^2] / 2*B
10 =55/60 * [B^2 – 2^2] / 2*B
9. A man can row a certain distance downstream in 2 hours and return the same distance in 6 hours. If the speed of current is 22 km/hr, find the speed of man in still water.
A. 44km/hr
B. 48 km/hr
C. 50 km/hr
D. 55 km/hr
Answer
A. 44km/hr
Explanation:
Use:
B = [tu + td] / [tu – td] * R
B = [6+2] / [6-2] * 22
B = 44
10. A man can row 9 3/5 km/hr in still water and he finds that it takes him twice as much time to row up than as to row down the same distance in river. The speed (km/hr) of the current is
A. 2
B. 2 1/2
C. 3 1/5
D. 5
Answer
C. 3 1/5
Explanation:
Let downstream time = t, then upstream time = 2t
B = [tu + td] / [tu – td] * R
48/5 = [2t+t] / [2t-t] * R
