Two professional drag racers are speeding down a 1/4-mile track. If the lead driver is traveling 1.738 feet for every 1.670 feet that the trailing car travels, and if the trailing car is going 198 miles per hour, how fast in miles per hour is the lead car traveling?
Use proportion:
1.67 ft : 1.738 ft = 198 mph : ?
200
Ratio of lead driver distance and trailing driver distance = StartFraction 1.716 Over 1.670 EndFraction
Speed of lead car = ratio times speed of trailing car = StartFraction 1.716 Over 1.670 EndFraction times 197 equals 202.4miles per hour
To find out how fast the lead car is traveling, we need to use the given information about the ratio between the distances covered by the lead car and the trailing car. Let's break down the problem step by step.
1. Convert 1/4 mile into feet:
- 1 mile = 5,280 feet
- Therefore, 1/4 mile = (1/4) x 5,280 = 1,320 feet
2. Determine the ratio of distance covered by the two cars:
- The trailing car travels 1.670 feet for every 1.670 feet the lead car travels.
- This can be written as 1.738:1.670.
3. Calculate the distance covered by the trailing car in feet:
- Since the trailing car is going 198 miles per hour, to find the distance covered in feet, we multiply the speed by the conversion factor:
- 198 mph x 5,280 feet/mile = 1,042,560 feet/hour
- But since we are interested in the distance covered in one-fourth of an hour (as they are on a 1/4-mile track), we divide by 4:
- 1,042,560 feet/hour / 4 = 260,640 feet
4. Determine the distance covered by the lead car:
- Using the ratio from step 2, for every 1.670 feet covered by the trailing car, the lead car covers 1.738 feet.
- Therefore, the distance covered by the lead car can be found by multiplying the distance covered by the trailing car (260,640 feet) by the ratio:
- 260,640 feet x (1.738/1.670) = 271,208.083 feet
5. Convert the distance covered by the lead car back into miles:
- To convert feet to miles, we divide by the conversion factor:
- 271,208.083 feet / 5,280 feet/mile = 51.36 miles
Therefore, the lead car is traveling at a speed of approximately 51.36 miles per hour.