SOLUTION: A tugboat traveling east at 40 mph is 20 mi from a harbor when another ship leaves the harbor traveling east at 50 mph. How long does it take the second tugboat to catch up to the

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: A tugboat traveling east at 40 mph is 20 mi from a harbor when another ship leaves the harbor traveling east at 50 mph. How long does it take the second tugboat to catch up to the       Log On


   

Question 1197148: A tugboat traveling east at 40 mph is 20 mi from a harbor when another ship leaves the harbor traveling east at 50 mph. How long does it take the second tugboat to catch up to the first ship?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = number of hours
y = distance from the harbor

Tugboat A is already 20 miles east of the harbor.
It travels 40 mph to the east
The equation for tugboat A is y = 40x+20

The equation for tugboat B is y = 50x since it travels east at a speed of 50 mph.

Set the right hand sides equal to one another to determine when the two boats meet up.
50x = 40x+20
50x-40x = 20
10x = 20
x = 20/10
x = 2

Answer: 2 hours

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Similar to the familiar formula for time,

(time) = (distance)/(rate)

there is the formula

(time) = (difference in distances)/(difference in rates)

In this problem, the distance to be made up by the second ship is 20 miles; the rate at which that distance is made up is 50-40 = 10mph. So the time required for the second ship to make of the distance is 20/10 = 2 hours.

ANSWER: 2 hours

Side note.... 40mph and 50mph are not reasonable speeds for large ships.