Distance, Speed, and Time A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6 s from the position shown in figure (a) to the position shown in figure (b)? [ Hint: Use feet and seconds instead of miles and hours.]
Distance, Speed, and Time A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6 s from the position shown in figure (a) to the position shown in figure (b)? [ Hint: Use feet and seconds instead of miles and hours.]
Solution Summary: The author explains that the speed of car to completely pass the truck is 80.66 mi/h.
Distance, Speed, and Time A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6 s from the position shown in figure (a) to the position shown in figure (b)? [Hint: Use feet and seconds instead of miles and hours.]
Expert Solution & Answer
To determine
To find: The speed of car to completely pass the truck.
Answer to Problem 70E
The speed of car to completely pass the truck is 80.66 mi/h.
Explanation of Solution
Given:
The length of car is 14 ft and the length of truck is 30 ft.
The speed of truck is 5 mi/h and time taken by car to pass the truck is 6 s.
Formula used:
Distance formula is,
distance=time×rate
Calculation:
Let the speed of car be x ft/s.
Speed of truck in ft/s,
50mi/h=50×52803600ft/s=73.33ft/s
Tabulate the given information into the language of algebra.
In words
In algebra
Speed of car
x
Effective speed
x−73.33
Total distance
30+14=44
Model the equation for the above information.
speed×time=distance(x−73.33)×6=44
Simplify the above equation for x,
6x−439.98=446x=483.98x=80.66
Thus, the speed of car to completely pass the truck is 80.66 mi/h.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.