Question

a whale is swimming due north at a speed of 30 miles per hour. just 5 miles away, a whale - watching tour boat is traveling south, directly toward the whale, at a speed of 46 miles per hour. how long will it be before they meet? if necessary, round your answer to the nearest minute. hours and minutes

Explanation:

Step1: Recall relative - speed formula

Since the whale and the boat are moving towards each other, the relative speed $v$ is the sum of their speeds. The speed of the whale $v_1 = 30$ miles per hour and the speed of the boat $v_2=46$ miles per hour. So, $v=v_1 + v_2=30 + 46=76$ miles per hour.

Step2: Use the distance - speed - time formula

The distance $d = 5$ miles. We know that $t=\frac{d}{v}$, where $t$ is the time, $d$ is the distance, and $v$ is the speed. Substituting $d = 5$ miles and $v = 76$ miles per hour, we get $t=\frac{5}{76}$ hours.

Step3: Convert hours to hours and minutes

To convert $\frac{5}{76}$ hours to minutes, we use the conversion factor $1$ hour $= 60$ minutes. So, $t=\frac{5}{76}\times60=\frac{300}{76}\approx3.947$ minutes.
We can also write $\frac{5}{76}$ hours as a mixed - number. $\frac{5}{76}$ hours $=0$ hours and $\frac{5}{76}\times60=\frac{300}{76}=3\frac{72}{76}=3\frac{18}{19}\approx3$ hours and $57$ minutes.

Answer:

0 hours and 4 minutes