Question

Searches related to Searches related to A motorboat travels 135 kilometers in 3 hours going upstream. It travels 183 kilometers going downstream in the same amount of time. What is the rate of the boat in still water? what is the rate of the current?

Answer 1

Answer:

$\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }$

Step-by-step explanation:

Hello, let's note v the rate of the boat and r the rate of the current. We can write the following

$\dfrac{135}{v-r}=3=\dfrac{183}{v+r}$

It means that

$135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}$

But we can as well use the second equation:

$3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}$

and then

$\boxed{v=\dfrac{159*8}{24}=53}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you