The barge passed 32 km along the river and, turning back, covered another 24 km, spending 4 hours for the entire journey.

The barge passed 32 km along the river and, turning back, covered another 24 km, spending 4 hours for the entire journey. Find your own barge speed if the river speed is 5 km / h.

Let us denote by the unknown variable x km / h – the own speed of the barge,

х + 5 km / h – speed of the barge along the river,

x – 5 km / h – speed of the barge against the stream of the river,

32 / x + 5 hours – the time the barge moves downstream,

24 / h – 5 hours – the time of movement of the barge against the current,

The total travel time is 4 hours. Let’s make the equation:

32 / (x + 5) + 24 / (x – 5) = 4

Let’s simplify the equation:

4x ^ 2 – 56x – 60 = 0

Roots: -1 and 15.

The speed cannot be negative numbers, which means the speed of the barge is 15 km per hour