Question

Sarah wants to arrive at her friends 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 per hour, the remainder of the drive at 65 miles per hour. How many minutes will it take Sarah to drive the first 15 miles? How many minutes will it take Sarah to drive the next 5 miles? How many hours will it take Sarah to drive the rest of the trip? What time should Sarah leave her house?

Answer 1

Answer:

(A) 15 minutes

(B) 10 minutes

(C) 1 hour

(D) 1:35 pm

Step-by-step explanation:

Question:

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.)

Solution:

Total distance = 85 miles

There are three segments of this trip, each one with its own speed.

1) 15 miles at 60 mph

2) 5 miles at 30 mph

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.

3) 65 miles at 65 mph

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