Question:
A speed of 30 miles per hour (mph) is equivalent to 48 kilometers per hour (km/h). Jane passes a sign stating that the speed limit is 50 km/h. What is the speed limit in miles per hour?
Answer:
The speed limit is 31.25 mph.
Step-by-step explanation:
1. Understand the given information:
- 30 mph = 48 km/h
- The speed limit is 50 km/h
- We need to convert 50 km/h to mph
2. Set up a proportion to convert km/h to mph:
30 mph / 48 km/h = x mph / 50 km/h
3. Cross multiply:
30 * 50 = 48x
4. Solve for x:
1500 = 48x
x = 1500 / 48
5. Calculate the result:
x = 31.25
Additional information:
This problem involves unit conversion and the use of proportions. The key is recognizing that the ratio between mph and km/h remains constant. Therefore, we can use the given equivalence (30 mph = 48 km/h) to set up a proportion and solve for the unknown speed in mph.
In real-world applications, it's important to note that speed limit signs are typically rounded to the nearest 5 or 10 units for practical reasons. So while the exact conversion is 31.25 mph, a actual speed limit sign in mph corresponding to 50 km/h would likely read 30 mph or 35 mph, depending on local regulations and rounding practices.
Step-by-step explanation:
well, 50 km/h is very close to 48 km/h.
so, the converted speed must also be very close to 30 mph (a little bit higher but very close).
in any case, there is the same conversion factor between 48 km/h and 30 mph on one hand and between 50 km/h and the converted x mph on the other hand.
so, the ratios must be equal :
48/30 = 50/x
48x/30 = 50
48x = 50×30 = 1500
x = 1500/48 = 375/12 = 125/4 = 31.25 mph
so, the speed limit is 31.25 mph.