A motorboat can maintain a constant speed of 15 mph relative to the water. The boat makes a trip upstream to a certain point in 15 minutes

constant-speed

#1

A motorboat can maintain a constant speed of 15 mph relative to the water. The boat makes a trip upstream to a certain point in 15 minutes; the return trip takes 10 minutes. What is the speed of the current?

Answer:

Let x is the speed of the current.
Using the following formula: s= v*t, where v - speed, t - time, s - distance
We have:
(15 - x) * 15 = (15 + x)*10
Then:
225 - 15x = 150 + 10x
And
25x = 75
So, x = 3 mph

Let speed of current be ‘w’ and distance be ‘d’. formula used:dist/time =speed
For upstream the boat runs against the stream so relative speed is 15-w,
we know that 'd/15-w=15/60 ------->1
For downstream the boat runs along with the stream so relative speed is 15+w,
we know that d/15+w=10/60 --------->2
1/2====>3/2=15+w/15-w
5w=45-30=15
hence, w=3mph

Let R be the speed of the boat and C be the speed of the current.
Upstream Time is 15 min and Downstream Time is 10 min.
Now R is given = 15mph and we have to find out C =?
Speed Upstream is R-C and Speed Downstream is R+C
Distance is Constant

Formula: Speed = Distance/Time => Distance = Speed*Time
Du = Dd
(R-C)*Tu = (R+C)*Td
(15-C)*15 = (15+c)*10
225 - 15C = 150 + 10C
75 = 25C
C = 3
Speed of the Current is 3mph