SOLUTION: Every day, Jane and Bill both drive to a parking lot, and then take a subway to get to work. Jane drives 30 km at 80 km/h, then takes a northbound subway that averages 25 km/h for

Question 1197382: Every day, Jane and Bill both drive to a parking lot, and then take a subway to get to work. Jane drives 30 km at 80 km/h, then takes a northbound subway that averages 25 km/h for 15 km while Bill drives 60 km at 100 km/h and then takes a southbound subway that averages 35 km/h for 15 km. It takes each of them 12 minutes to change from car to subway, and they arrive at the same destination at 8:30 a.m. At what time, to the nearest minute, does the earliest of them leave home?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

kph = kilometers per hour

Jane drives 30 km at 80 kph.

So,
distance = rate*time
time = distance/rate
time = (30 km)/(80 kph)
time = 3/8 hour
She spent 3/8 of an hour driving to the parking lot.

Then she takes 12 minutes, aka 12/60 = 1/5 of an hour, to go from her car to the subway.
So far the duration is (3/8)+(1/5) = (15/40)+(8/40) = 23/40 of an hour.

Then she takes a subway which travels at a rate of 25 kph and travels a distance of 15 km
time = distance/rate
time = (15 km)/(25 kph)
time = 3/5 hour

Add this to the duration
(23/40)+(3/5) = (23/40)+(24/40) = 47/40
Put another way
3/8 + 1/5 + 3/5 = 47/40

Her total duration is 47/40 of an hour.
1/40 of an hour is (1/40)*60 = 1.5 minutes exactly.
47/40 of an hour is 47*(1/40 hr) = 47*(1.5 min) = 70.5 minutes exactly

Round up to the nearest minute to get 71 minutes.

71 min = 60 min + 11 min

The total duration is 1 hr + 11 min when rounding to the nearest minute.

She arrives at her destination at 8:30 AM
Subtract off 1 hour to get to 7:30 AM
Subtract off a further 11 minutes to get to 30-11 = 19
I.e. 7:30 AM rewinds back to 7:19 AM after subtracting off those additional 11 minutes.

Jane needs to leave her home at 7:19 AM

----------------------------------------------------------

Let's move our attention to Bill.

He travels 60 km at 100 kph when driving.
time = distance/rate
time = (60 km)/(100 kph)
time = 3/5 hour

He takes 12 min = 1/5 hour going from his car to the subway

His subway travels 15 km at a speed of 35 kph
time = distance/rate
time = (15 km)/(35 kph)
time = 3/7 hour

The three durations of each sub-interval are
3/5 hour ... home to parking lot
1/5 hour ... car to subway
3/7 hour ... subway to work

Add up those fractions to get the total duration he travels
3/5+1/5+3/7
4/5+3/7
28/35+15/35
43/35

Multiply by 60 to convert this to purely minutes only
43/35 hr = (43/35)*60 = 73.714 min approximately
Let's round this up to the nearest minute to get 74 minutes.

74 min = 60 min + 14 min
74 min = 1 hr + 14 min

Start at 8:30 AM
Subtract off 1 hour to get to 7:30 AM
Subtract off another 14 min to get to 7:16 AM

Or you could note the gap between durations 71 minutes (Jane) and 74 minutes (Bill) is 74-71 = 3 minutes.
Therefore, Bill needs to leave 3 minutes earlier than Jane does.

----------------------------------------------------------

Answers:
Jane = 7:19 AM
Bill = 7:16 AM

RELATED QUESTIONS
Every day, Jane and Bill both drive to a parking lot, and then take a subway to get to... (answered by MathLover1)

Every day Jane and Bill both drive to a parking lot, and then take the subway to get to... (answered by josmiceli)

Every day Jane and Bill both drive into a parking lot, and then take a subway to get to... (answered by ikleyn,math_tutor2020)

Roman and Paul are driving on the same highway and both drive at a constant speed. Roman... (answered by ikleyn)

jane runs three and a half km in 70 minutes . How long will it take her to run 9 km ? (answered by skartikey)

Peggy drives to town at a rate of 40 km/h. How fast must she drive in order to average 80 (answered by ikleyn,Alan3354)

Peggy drives to town at a rate of 40 km/h. How fast must she drive BACK in order to... (answered by Alan3354,ikleyn)

Jill travels to work in one hour and 30 minutes. Jane travels to work in one hour and 20... (answered by ewatrrr)

Neville and Carl both leave Perth at the same time to go on holidays. Neville travels by... (answered by ikleyn)