Answer:
(A) 15 minutes
(B) 10 minutes
(C) 1 hour
(D) 1:35 pm
Step-by-step explanation:
<em>Question:</em>
Sarah wants to arrive at her friend’s wedding at 3:00 PM. The distance from Sarah’s house to the wedding is 85 miles. Based on usual traffic patterns, Sarah predicts she can drive the first 15 miles at 60 miles per hour, the next 5 miles at 30 miles per hour, and the remainder of the drive at 65 miles per hour.
(A) how many minutes will it take Sarah to drive the first 15 miles?
(B) how many minutes will it take Sarah to drive 5 miles?
(C) how many hours will it take Sarah to drive the rest of the trip?
(D) what time should Sarah leave her house? (Give your answer using standard hour:minute clock format.)
<em>Solution:</em>
Total distance = 85 miles
There are three segments of this trip, each one with its own speed.
<em>1) 15 miles at 60 mph</em>
<em>2) 5 miles at 30 mph</em>
Up to here, the distance is 15 miles + 5 miles = 20 miles.
The total distance is 85 miles, so the last segment of the trip is 85 miles - 20 miles = 65 miles.
<em>3) 65 miles at 65 mph</em>
The equation for speed is:
speed = distance/time
Now we solve it for time:
speed * time = distance
time = distance/speed
To find a time, divide the distance by the speed.
Part (A)
distance = 15 miles; speed = 60 mph; find time
time = distance/speed = 15 miles/60 mph = 0.25 hours
Since 1 hour = 60 minutes,
time = 0.25 hours * 60 minutes/hour = 15 minutes
Part (B)
distance = 5 miles; speed = 30 mph; find time
time = distance/speed = 5 miles/30 mph = 1/6 hour
Since 1 hour = 60 minutes,
times = 1/6 hour * 60 minutes/hour = 10 minutes
Part (C)
distance = 65 miles; speed = 65 mph; find time
time = distance/speed = 65 miles/65 mph = 1 hour
Part (D)
The driving times for the three segments are 15 minutes, 10 minutes, and 1 hour. The total driving time is
15 minutes + 10 minutes + 1 hour = 1 hour and 25 minutes
Now we subtract 1 hour 25 minutes from 3:00 pm.
3:00 pm is the same as 2:60 pm
2:60 pm - 1:25 = 1:35 pm
She needs to leave at 1:35 pm
