UOM A ship is traveling at 40 knots. A train is traveling at 50 mph. Convert the speeds. (1 knot = 1.15 miles per hour) Round to the nearest tenth if necessary. The ship’s speed is The train’s speed is
The Correct Answer and Explanation is:
To convert the speeds from one unit of measurement to another, we use the conversion factor provided: 1 knot=1.15 mph1 \, \text{knot} = 1.15 \, \text{mph}1knot=1.15mph. Let’s convert the ship’s speed first and then the train’s speed.
Ship’s Speed Conversion:
The ship is traveling at 40 knots. To convert this to miles per hour, we multiply the number of knots by the conversion factor:Ship’s Speed in mph=40 knots×1.15 mph/knot=46 mph\text{Ship’s Speed in mph} = 40 \, \text{knots} \times 1.15 \, \text{mph/knot} = 46 \, \text{mph}Ship’s Speed in mph=40knots×1.15mph/knot=46mph
So, the ship’s speed is 46 mph.
Train’s Speed Conversion:
Next, we need to convert the train’s speed from miles per hour to knots. The conversion factor is the reciprocal of the one used above: 1 mph=11.15 knots1 \, \text{mph} = \frac{1}{1.15} \, \text{knots}1mph=1.151knots.
We divide the train’s speed in miles per hour by the conversion factor:Train’s Speed in knots=50 mph1.15 mph/knot≈43.5 knots\text{Train’s Speed in knots} = \frac{50 \, \text{mph}}{1.15 \, \text{mph/knot}} \approx 43.5 \, \text{knots}Train’s Speed in knots=1.15mph/knot50mph≈43.5knots
So, the train’s speed is approximately 43.5 knots.
Summary:
- The ship’s speed is 46 mph.
- The train’s speed is 43.5 knots.
By converting both speeds, we can compare the two vehicles’ velocities in the same unit, giving us a clearer understanding of their relative speeds.
