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A Boat covers a distance of 44 km downstream and 42 km upstream in 10 hours, if the boat traveled 38.5 km downstream and 63 km upstream, it will take 12.5 hours. Find the speed of boat and stream.
1. 9 km/h and 2 km/h
2. 7 km/h and 2 km/h
3. 11 km/h and 3 km/h
4. 8 km/h and 1.5 km/h

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Correct Answer - Option 1 : 9 km/h and 2 km/h

Given:

Time taken to cover 44 km downstream and 42 km upstream = 10 hours

Time taken to cover 38.5 km downstream and 63 km upstream = 12.5 Hours

Formula Used:

Time = Distance/Speed

Downstream Speed (D) = Speed of Boat (x) + Speed of Stream (y)

Upstream Speed (U) = Speed of Boat (x) - Speed of Stream (y)

Speed of Boat = (D + U)/2

Speed of Stream = (D - U)/2

Calculation:

Let the downstream speed be D and upstream speed be U

(44/D) + (42/U) = 10      ____(i)

(38.5/D) + (63/U) = 12.5      ____(ii)

Multiply equation i by 3 and equation ii by 2

(132/D) + (126/U) = 30      ____(i)

(77/D) + (126/U) = 25      ____(ii)

Subtract equation ii from equation i

[(132/D) + (126/U) = 30] – [(77/D) + (126/U) = 25]

⇒ (55/D) = 5

⇒ D = (55/5)

⇒ D = 11 km/h

Putting value of D in equation i

(44/11) + (42/U) = 10

⇒ 4 + (42/U) = 10

⇒ (42/U) = 6

⇒ U = 42/6 = 7 km/h

Speed of Boat = (11 + 7)/2

⇒ Speed of Boat = 9 km/h

Speed of Stream = (11 – 7)/2

⇒ Speed of Stream = 2 Km/h

∴ The speed of boat and stream is 9 km/h and 2 km/h respectively.

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