The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.

Matching exercise

    
Match the items on the right to the items on the left.
STEP 1
STEP 2
STEP 3
STEP 4
STEP 5
STEP 6
Speed = distance/time


Let the speed of boat be ‘a’ and speed of stream be ‘b’


Relative speed of boat going upstream = a – b


Relative speed of boat going downstream = a + b
Given, boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. we know, time =speed/distance
Q3a.png
Eq 1 and 2 becomes⇒ 30 u + 44 v = 10Take 2 common out of above equation⇒ 15 u + 22 v - 5 = 0 ..... (3)and40 u + 55 v - 13 = 0 ..... (4)Solve the equations by cross multiplication method
Q3b.pngQ3c.png
⇒ a- b = 5 .... (4) a + b = 11 .... (5)Add eq 4 and 5 to geta - b + a + b = 5 + 11⇒ 2a = 16⇒ a = 8 Substitute value of a in eq 4 we get,8 - b = 5⇒ b = 8 - 5⇒ b = 3Speed of boat = 8 km/hr and speed of stream = 3 km/hr