Sarah wants to arrive at her friend's wedding at 3:00 PM. The distance from Sarah's house to the wedding is 95 miles. Based on usual traffic patterns, Sarah predicts she can drive the first 25 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 25 miles? (b) How many minutes will it take Sarah to drive the next 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?
All your questions ask for "time"
in these questions, time = distance/rate
watch for units, some times are in minutes, others in hours
a) distance = 25 miles
rate = 60 mph
time = 25/60 hours = 5/12 hours OR 25 minutes
(realize that at 60 miles/hour, you would be going 1 mile per 1 minute.)
b) try the rest
(a) To find the time it will take Sarah to drive the first 25 miles, we will use the formula: time = distance / speed.
Given that the distance is 25 miles and the speed is 60 miles per hour, we can calculate the time as follows:
time = 25 miles / 60 miles per hour
Converting 60 minutes per hour to minutes, we get:
time = 25 miles / (60 miles / 60 minutes)
time = 25 miles / (60/60)
time = 25 miles / 1
time = 25 minutes
Therefore, it will take Sarah 25 minutes to drive the first 25 miles.
(b) To find the time it will take Sarah to drive the next 5 miles, we will use the same formula: time = distance / speed.
Given that the distance is 5 miles and the speed is 30 miles per hour, we can calculate the time as follows:
time = 5 miles / 30 miles per hour
Converting 60 minutes per hour to minutes, we get:
time = 5 miles / (30 miles / 60 minutes)
time = 5 miles / (30/60)
time = 5 miles / 0.5
time = 10 minutes
Therefore, it will take Sarah 10 minutes to drive the next 5 miles.
(c) The distance for the rest of the trip is 95 - 25 - 5 = 65 miles.
Sarah predicts she will be driving at 65 miles per hour for the remaining distance.
To find the time it will take Sarah to drive the remaining distance, we will use the formula: time = distance / speed.
Given that the distance is 65 miles and the speed is 65 miles per hour, we can calculate the time as follows:
time = 65 miles / 65 miles per hour
time = 1 hour
Therefore, it will take Sarah 1 hour to drive the rest of the trip.
(d) To find the total time it will take Sarah to get to her friend's wedding, we need to add the time for each part of the trip:
25 minutes (first 25 miles) + 10 minutes (next 5 miles) + 60 minutes (rest of the trip)
Total time = 25 + 10 + 60 = 95 minutes
Since there are 60 minutes in an hour, we need to convert the total time to hours and minutes:
Total time = 95 minutes / 60 minutes per hour
Total time = 1 hour and 35 minutes
Sarah wants to arrive at 3:00 PM, so she needs to leave her house 1 hour and 35 minutes before that.
Therefore, Sarah should leave her house at 1:25 PM.
(a) To calculate the time it will take Sarah to drive the first 25 miles, we can use the formula: time = distance / speed. Given that the distance is 25 miles and the speed is 60 miles per hour, we can substitute the values into the formula: time = 25 miles / 60 miles per hour.
To convert the time from hours to minutes, we need to multiply the result by 60, as there are 60 minutes in an hour. So, the time in minutes will be: time = (25 miles / 60 miles per hour) * 60 minutes per hour.
Simplifying the expression: time = (25/60) * 60 = 25 minutes.
Therefore, it will take Sarah 25 minutes to drive the first 25 miles.
(b) Similarly, to calculate the time it will take Sarah to drive the next 5 miles, we can use the same formula: time = distance / speed. Given that the distance is 5 miles and the speed is 30 miles per hour, we can substitute the values into the formula: time = 5 miles / 30 miles per hour.
To convert the time from hours to minutes, we need to multiply the result by 60. So, the time in minutes will be: time = (5 miles / 30 miles per hour) * 60 minutes per hour.
Simplifying the expression: time = (5/30) * 60 = 10 minutes.
Therefore, it will take Sarah 10 minutes to drive the next 5 miles.
(c) To calculate the time it will take Sarah to drive the remainder of the trip, we need to know the distance and the speed for that portion of the journey. The total distance to the wedding is 95 miles, and she has already driven the first 25 miles and the next 5 miles, which adds up to 30 miles. Therefore, the remaining distance is 95 miles - 30 miles = 65 miles.
Given that she will be driving the rest of the trip at a speed of 65 miles per hour, we can use the formula: time = distance / speed. Substituting the values: time = 65 miles / 65 miles per hour.
We don't need to convert the time from hours to minutes since the question asks for the time in hours.
So, the time it will take Sarah to drive the rest of the trip is: time = 65 miles / 65 miles per hour = 1 hour.
Therefore, it will take Sarah 1 hour (or 60 minutes) to drive the rest of the trip.
(d) To determine what time Sarah should leave her house, we need to add up the times it will take her to drive each portion of the trip.
- She will take 25 minutes to drive the first 25 miles.
- She will take 10 minutes to drive the next 5 miles.
- She will take 60 minutes to drive the remainder of the trip.
Adding up these times: 25 minutes + 10 minutes + 60 minutes = 95 minutes.
Therefore, Sarah should leave her house 95 minutes (or 1 hour and 35 minutes) before 3:00 PM, assuming there are no other factors to consider like finding parking or delays.