Can someone help me with a formula for this?
A container ship left the Azores and
traveled north. An aircraft carrier left two
hours later traveling 5 km/h faster in an
effort to catch up to it. After eight hours
the aircraft carrier finally caught up.
What was the container ship's average
speed?
rate of container ship ---- x km/h
rate of carrier ------- x+5 km/h
after 8 ours, carrier caught up, they went the same distance.
10x = 8(x+5)
solve for x
To find the container ship's average speed, you can use the formula:
Average Speed = Total Distance / Total Time
Now let's break down the problem and gather the necessary information:
1. The aircraft carrier left two hours later than the container ship.
2. After eight hours, the aircraft carrier caught up to the container ship.
3. The aircraft carrier traveled 5 km/h faster than the container ship.
Let's assume the container ship's speed as "x" km/h.
Since the aircraft carrier left two hours later and caught up after eight hours, it traveled for a total of 8 - 2 = 6 hours.
During that time, the aircraft carrier traveled at a speed of (x + 5) km/h.
Now, we need to calculate the distance traveled by both the container ship and the aircraft carrier and set them equal to each other since they reached the same point:
Distance traveled by the container ship = Distance traveled by the aircraft carrier
To find the distance traveled, we can use the formula:
Distance = Speed × Time
For the container ship, the distance traveled is:
Distance = x km/h × 8 hours
For the aircraft carrier, the distance traveled is:
Distance = (x + 5) km/h × 6 hours
Therefore, we can set up the equation:
x km/h × 8 hours = (x + 5) km/h × 6 hours
Now, solve the equation to find the value of "x." Once you have the value of "x," it will represent the container ship's average speed.