SOLUTION: Pratap Puri rowed 14 miles down a river in 2 ​hours, but the return trip took him 3 1/2 one half hours. Find the rate Pratap can row in still water and find the rate of the

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Question 1049571: Pratap Puri rowed 14 miles down a river in 2 ​hours, but the return trip took him 3 1/2 one half hours. Find the rate Pratap can row in still water and find the rate of the current
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
                 SPEED         TIME        DISTANCE

DOWN RIVER        r+c            2          14

UP RIVER          r-c                  14


Constant Travel Rate Rule, RT=D.
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.
Pratap Puri rowed 14 miles down a river in 2 hours, but the return trip took him 3 1/2 one half hours.
Find the rate Pratap can row in still water and find the rate of the current
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

2 hours = 2 hours;    hours =  hours.

The standard way of solving such problem is this. 
From the condition you have these two equations

    = u + v,   (1)

 = u - v.   (2)

The left side of the equation (1) is the speed of the boat relative the bank of the river when rowing with the current, 
and it is the sum of the rate of the boat in still water and the current rate.

The left side of the equation (2) is the speed of the boat relative the bank of the river when rowing against the current, 
and it is the difference of the rate of the boat in still water and the current rate.

Simplify the equations (1) and (2):

u + v = 7,     (3)
u - v = 4.     (4)

Now add the equations (3) and (4). You will get

2u = 7 + 4 = 11,  or  u =  = 5.5.

Thus you just found the speed of the boat in still water. It is 5.5 miles per hour.

Now it is easy to find the speed of current. It is

v = 7 - u = 7 - 5.5 = 1.5 miles per hour.

Check.  The boat' speed with the current is 5.5 + 1.5 = 7 mph.
        The time for down a river trip is  = 2 hours.

        The boat' speed against the current is 5.5 - 1.5 = 4 mph.
        The time for the return trip is  =   hours.

        The solution was checked and found to be correct.


Answer.  The speed of the boat in still water is 5.5 mph.  The speed of current is 1.5 mph.

Solved.


It is a typical Upstream and Downstream round trips word problem.
You can find similar fully solved similar problems on upstream and downstream round trips with detailed solutions in the lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Selected problems from the archive on the boat floating Upstream and Downstream

Read them attentively and learn how to solve this type of problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Travel and Distance problems" of the section "Word problems" .


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Pratap Puri rowed 14 miles down a river in 2 ​hours, but the return trip took him 3 1/2 one half hours. Find the rate Pratap can row in still water and find the rate of the current
Average speed down-river: 

Let speed in still water be S, and rate of current, C

Down-river equation: S + C = 7 ------- eq (i)



Average speed up-river: 

Up-river equation: S - C = 4 ------- eq (ii)

2S = 11 -------- Adding eqs (ii) & (i)

S, or rate in still water = , or 



5.5 + C = 7 ------- Substituting 5.5 for S in eq (i)

C, or rate of current = 7 - 5.5, or  

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