SOLUTION: The driving distance between Boston and NYC is 220 miles. At 10:00am, Alecia starts out driving from Boston to NYC and drives at an average speed of 70MPH. At 11:00am that same d

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Question 1163254: The driving distance between Boston and NYC is 220 miles. At 10:00am, Alecia starts out driving from Boston to NYC and drives at an average speed of 70MPH. At 11:00am that same day, Burt starts out driving from NYC to Boston on the same route (opposite direction) and he drives at an average speed of 65MPH. Assuming neither makes any stops along the way: 1) at what time will they pass one another; and 2) how far will each have driven at that point?
Found 3 solutions by solver91311, jim_thompson5910, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


If the one going 70 mph leaves at 10 and the other leaves at 11 am, the first one will have travelled 70 miles in that first hour, so that when they are both moving, they will start at 150 miles apart. Since they are traveling in opposite directions, their speed of approach is the sum of their speeds, namely 135 miles per hour. So they will meet at hours after 11 am, or 12:06:40 pm. A travels a total of 70 miles plus hours times 70 miles per hour. B travels a total of hours times 65 miles per hour.


John

My calculator said it, I believe it, that settles it
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Part 1)

t = number of hours Alecia has been driving
t - 1 = number of hours Burt has been driving (he starts 1 hour later, so he has been driving 1 hour less)

using the formula
distance = rate*time
we can form the expression 70t to represent how far (in miles) Alecia has driven after t hours.

Burt's distance expression is 65(t-1)

The two distance expressions must add to 220 in order for the two drivers to meet
70t + 65(t-1) = 220
70t + 65t-65 = 220
135t-65 = 220
135t = 220+65
135t = 285
t = 285/135
t = 2.1111111 approximately (the 1's repeat forever)
Multiply this with 3600 to get
2.1111111*3600 = 7599.99996 and that rounds to 7600
The rounding error occurs because the calculator can only hold so much data.

Therefore, 7600 seconds have elapsed from the time Alecia started driving to the point where the two drivers meet.

Convert from pure seconds to hours,minutes,seconds format
7600 seconds = 7560 seconds + 40 seconds
7600 seconds = (7560/60) minutes + 40 seconds
7600 seconds = 126 minutes + 40 seconds
7600 seconds = 120 minutes + 6 minutes + 40 seconds
7600 seconds = (120/60) hours + 6 minutes + 40 seconds
7600 seconds = 2 hours + 6 minutes + 40 seconds
7600 seconds = 2 hours, 6 minutes, 40 seconds

They will meet 2 hours, 6 minutes, 40 seconds after 10:00 AM

Perform clock arithmetic to get
10:00:00 + 02:06:40 = (10+2):(0+6):(0+40)
10:00:00 + 02:06:40 = 12:06:40

Starting at 10:00 AM, and fast forwarding the duration of time found above, we arrive at 12:06:40 PM. This is the time when the two drivers meet.

Answer = 12:06:40 PM

==========================================================
Part 2)

Use the t value found back in part 1) to get
A = Alecia's distance traveled
A = 70*t
A = 70*2.11111111111111
A = 147.777777777778 miles approximately

and
B = Burt's distance traveled
B = 65(t-1)
B = 65(2.11111111111111-1)
B = 72.222222222222 miles approximately

Note how
A+B = 147.777777777778+72.222222222222 = 220
to help confirm we have the proper t value

Answer: Alecia has driven about 147.777777777778 miles while Burt has driven about 72.222222222222 miles

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The driving distance between Boston and NYC is 220 miles. At 10:00am, Alecia starts out driving from Boston to NYC and drives at an average speed of 70MPH. At 11:00am that same day, Burt starts out driving from NYC to Boston on the same route (opposite direction) and he drives at an average speed of 65MPH. Assuming neither makes any stops along the way: 1) at what time will they pass one another; and 2) how far will each have driven at that point?
Let time Burt takes to get to the PASSING point be T
Then time Alecia takes to get to the PASSING point is: T + 1 
We then get the following DISTANCE equation: 65T + 70(T + 1) = 220
65T + 70T + 70 = 220
135T = 150
Time Burt takes to get to the PASSING point, or 
                                                
                                                

This gives us a time, from Burt starts driving, of: 1 hour, 6 minutes, 40 seconds.

1 hour, 6 minutes, and 40 seconds AFTER Burt leaves, at 11:00 a.m., is: 


With Alecia starting out at 10:00 a.m., 1 hour before Burt, time she takes to get to PASSING point = 

With Burt taking , travelling at 65 mph, distance he travels to get to PASSING point = 

With Alecia taking , travelling at 70 mph, distance she travels to get to PASSING point =

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