LettingInModdd
Answered

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The speed of a river boat is 40 km/h and the rate of flow of the river is 8 km/h. Moving along the same direction as the flow of the river, the boat traveled 240 km. Calculate the distance the boat could travel going against the stream in the same time period.​

Sagot :

kumikofan

Hello, LettingInModdd! I will be solving your problem today.

Your math problem is:

  • The speed of a river boat is 40 km/h and the rate of flow of the river is 8 km/h. Moving along the same direction as the flow of the river, the boat traveled 240 km. Calculate the distance the boat could travel going against the stream in the same time period.

Note:

When the boat is moving along with the stream, the river's rate of flow is added to the boat's speed. However, when the boat is moving against the stream, the river's rate of flow is subtracted from the boat's speed.

Given:

We are given the following values:

  • the speed of a boat in still water is 40 km/h.
  • the rate of flow of the river is 8 km/h.
  • moving along the same direction as the flow of the river, the boat traveled a distance of 240 km.

We let the expression x + 8 as the speed of the boat moving in the same direction as the flow of the river, and x - 8 as the speed of the boat moving against (the opposite direction as) the flow of the river, where x is the speed of the boat in still water.

Given that the speed of a boat in still water is 40 km/h,

  • the speed of the boat moving in the same direction as the stream is 40 km/h + 8 km/h = 48 km/h.
  • the speed of the boat moving against the stream is 40 km/h - 8 km/h = 32 km/h.

Solve:

Given that the distance of the boat moving along with the stream at a certain amount of time is 240 km,

  • [tex] \sf time = \frac{distance}{speed} [/tex]

  • [tex] \sf time = \frac{240\:km}{48\:km/h} [/tex]

  • [tex] \sf time = 5\:h [/tex]

At the same time period (t = 5 h), calculate the distance the boat could travel going against the stream.

  • [tex] \sf distance = speed \cdot time [/tex]

  • [tex] \sf distance = 32\:km/h \cdot 5\:h [/tex]

  • [tex] \large \green {\sf distance = 160\:km} [/tex]

Answer:

Therefore, the distance the boat could travel going against the stream is 160 km.

Hope this helps! You're welcome! ~azure

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