Q. A boat can travel at 10 km/h in still water. If it is moving downstream in a river flowing at 5 km/h, what is the speed of the boat relative to the riverbank?
A.5 km/h
B.10 km/h
C.15 km/h
D.20 km/h
Solution
Speed downstream = Speed of boat + Speed of river = 10 km/h + 5 km/h = 15 km/h.
Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?
A.8 km/h
B.12 km/h
C.16 km/h
D.20 km/h
Solution
Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.
Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 3 km/h, what is the speed of the boat relative to the riverbank?
A.9 km/h
B.12 km/h
C.15 km/h
D.3 km/h
Solution
Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.
Q. A boat can travel at 12 km/h in still water. If it is moving downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?
A.8 km/h
B.12 km/h
C.16 km/h
D.4 km/h
Solution
Speed of boat relative to riverbank = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.
Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstream and 1.5 hours to travel downstream, what is the speed of the current?
A.2 km/h
B.3 km/h
C.4 km/h
D.5 km/h
Solution
Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. (2 hours)(15 - x) = (1.5 hours)(15 + x). Solving gives x = 3 km/h.
Q. A boat travels 30 km upstream and 30 km downstream in a total time of 6 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the current?
A.2 km/h
B.3 km/h
C.4 km/h
D.5 km/h
Solution
Let speed of current = x. Time upstream = 30/(10-x), downstream = 30/(10+x). Total time = 6 hours. Solving gives x = 2 km/h.
Q. A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?
Q. A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
A.8 km/h
B.10 km/h
C.14 km/h
D.6 km/h
Solution
Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.
Q. A car is moving at 80 km/h and a motorcycle is moving at 100 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.20 km/h
B.180 km/h
C.100 km/h
D.80 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 100 km/h - 80 km/h = 20 km/h.
Q. A car is moving at 80 km/h and a motorcycle is moving at 60 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.20 km/h
B.60 km/h
C.80 km/h
D.140 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind).
Q. A car travels at a speed of 80 km/h and a bike travels at 60 km/h. If they start from the same point and travel in the same direction, how far apart will they be after 1 hour?
A.20 km
B.10 km
C.30 km
D.40 km
Solution
Relative speed = 80 - 60 = 20 km/h. Distance apart after 1 hour = 20 km.
Q. A car travels at a speed of 80 km/h and a truck travels at 60 km/h in the same direction. How far apart will they be after 2 hours if they start together?
A.20 km
B.40 km
C.60 km
D.80 km
Solution
Relative speed = 80 - 60 = 20 km/h. Distance = speed * time = 20 * 2 = 40 km.
Q. A cyclist is moving at 15 m/s and a pedestrian is walking at 5 m/s in the same direction. What is the speed of the cyclist relative to the pedestrian?
A.10 m/s
B.15 m/s
C.5 m/s
D.20 m/s
Solution
Relative speed = Speed of cyclist - Speed of pedestrian = 15 m/s - 5 m/s = 10 m/s.
