rachel allows herself one hour to reach a sales appointment 50 miles away. after she has driven 30 miles, she realizes that she must increase her speed by 15mph in order to arrive on time. what was her speed for the first 30 miles?
Rachel allows herself one hour to reach a sales appointment 50 miles away. after she has driven 30 miles, she realizes that she must increase her speed by 15mph in order to arrive on time. what was her speed for the first 30 miles?
The time to drive the first 30 miles is T1 = 30/V1.
The time to drive the last 20 miles is T2 = 20/(v1 + 15)
wHAT DO YOU KNOW ABOUT t1 + t2?
that it equals 60 minutes?
To solve this problem, we can use the concept of average speed. Average speed is calculated by dividing the total distance traveled by the total time taken.
Let's break down the information given:
- Rachel has one hour to reach her sales appointment.
- She has already driven 30 miles.
Now, let's calculate the time it would take Rachel to drive the remaining 20 miles at her increased speed.
Given:
- Distance traveled: 30 miles
- Remaining distance: 20 miles
Rachel originally allocated one hour for the entire journey. However, she realizes she needs to increase her speed for the remaining distance in order to arrive on time. This means the remaining 20 miles must be covered in less than one hour.
Since Rachel increased her speed by 15 mph, we can calculate the time it would take her to cover the remaining distance of 20 miles at this increased speed.
Time = Distance / Speed
Time for remaining 20 miles = 20 miles / (original speed + 15 mph)
Now, we can calculate the speed for the first 30 miles.
Time = Distance / Speed
Using the equation above, we can rearrange it to solve for Speed:
Speed = Distance / Time
Speed for the first 30 miles = 30 miles / (total time - time for remaining 20 miles)
Let's plug in the values we have:
Time for remaining 20 miles = 20 miles / (original speed + 15 mph)
Total time = 1 hour
Speed for the first 30 miles = 30 miles / (total time - time for remaining 20 miles)
Now we can substitute the values back into the equation and solve:
Time for remaining 20 miles = 20 miles / (original speed + 15 mph)
Total time = 1 hour = 60 minutes
Speed for the first 30 miles = 30 miles / (total time - time for remaining 20 miles)
Now, solving the equation will give us the speed for the first 30 miles.