Question

A boat goes 30 km upstream and 44 km

downstream in 10 hours. In 13 hour it can go

40 km upstream and 55 km downstream. If

speed of the boat in still water is x km/hr and

speed of stream be y km/hr, then -

(1) x = 8 (2) y = 4

(3) x = 3 (4) y = 8

FIRST ANSWER WILL BE BRAINLIEST.⏰⏰⏰

Answer 1

Answer:

x = 3 kmph

Step-by-step explanation:

Solving for downstream,

for 30 km up + 44 km down, time required = 10 hrs

for 40 km up + 55 km down, time required = 13 hrs

lcm of 30 and 40 is 120.

for 4 × (30 km up + 44 km down), time required = 4 × 10 = 40 hrs

i.e. for 120 km up + 176 km down, time required = 40 hrs

for 3 × (40 km up + 55 km down), time required = 3 × 13 = 39 hrs

i.e. for 120 km up + 165 km down, time required = 39 hrs

for (120 km up + 176 km) - (120 km up + 165 km down),

time required = 40 -39 = 1 hr

i.e. for 120 km up - 120 km up + 176 km down - 165 km down,

time required = 1 hr

i.e. for 11 km down, time required = 1 hr

downstream speed = 11 kmph

value of downstream speed in any of the initial equations.

time required for travelling 44 km downstream ,

= $\frac{44}{downstream speed}$

=  $\frac{44}{11}$ = 4 hrs

for 30 km up + 44 km down, time required = 10 hrs

for 30 km up,

time required = 10 - time required for 44 km down

= 10 -4 = 6 hrs

upstream speed =  $\frac{30}{6}$ = 5 kmph

speed of boat in still water = $\frac{downstream speed + upstream speed}{2}$

= $\frac{5 + 1}{2}$

= $\frac{6}{2}$

= 3 kmph

speed of boat in stream = $\frac{downstream speed - upstream speed}{2}$

= $\frac{5 - 1}{2}$

= $\frac{4}{2}$

= 2 kmph