Question

Two boats left an island at the same time to return to the same home port. Their rates of speed differ by 4km/h. The faster boat reached the port in 3 hours. The other boat took 30 minutes longer. Find the average speed of each boat.

Answer 1

Answer:

Average speed of the two boats are 28 km/hr. and 24 km/hr.

Step-by-step explanation:

Let the average speed of the boat with larger speed is x km/h and that of the other boat is y km/h.

Now, given that x - y = 4 ...... (1)

If the distance, that the first boat covers in 3 hrs. is d km then the second boat covers d km in 3.5 hrs.

Therefore, $x =\frac{d}{3}$ and $y = \frac{d}{3.5}$

Now, from equation (1), we can get $\frac{d}{3} -\frac{d}{3.5} =4$

⇒ $d(\frac{0.5}{3 \times 3.5} ) =4$

⇒ $x= \frac{d}{3} = \frac{4 \times 3.5}{0.5} =28$ km/hr.

Again, $y= \frac{d}{3.5} =\frac{4 \times 3}{0.5}= 24$ km/hr.

Therefore, the average speed of the two boats is 28 km/hr. and 24 km/hr. (Answer)