A steamer takes 3 hours to go 4 km upstream and 40 km downstream The same steamer takes 6 - Maths - Pair of Linear Equations in Two Variables

Question

A steamer takes 3 hours to go 4 km upstream and 40 km downstream
The same steamer takes 6 5 hours to go 36 km upstream and 32 km
downstream Find the speed of steamer in still water and speed of
the stream

Saksham Tolani · Accepted Answer

Dear student,

Let the rate of upstream=x km/h and the rate of downstream=y km/hCase 1: When steamer goes 4km upstream and 40km downstream in 3 hours4x+40y=3     
(1)Case 2: When steamer goes 36km upstream and 32km downstream in 6
5 hours36x+32y=6 5     
(2)Multiply eq(1) by 9, we get36x+360y=27      
(3)Subtract (2) from (3), we get36x+360y-36x-32y=27-6
5⇒328y=20
5⇒y=16km/hPut the value of y in (1), we get4x+4016=3  ⇒4x=3-52⇒4x=12⇒x=8km/hrNow, speed of boat in still water=12Speed of steamer upstream+Speed of steamer downstream=128+16km/h=12km/h
Regards!

A steamer takes 3 hours to go 4 km upstream and 40 km downstream. The same steamer takes 6.5 hours to go 36 km upstream and 32 km downstream. Find the speed of steamer in still water and speed of the stream.