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IMO
3 hours
6 hours




Arden spent his vacation touring London and Paris. On his first day in London, he boarded a double-decker bus, which traveled 30 miles through the city at an average speed of 15 miles per hour. He then boarded a tour bus and traveled 30 miles outside the city. The bus stopped at a museum outside of London for lunch for 60 minutes before returning to its original location in the city. The bus traveled an average of 60 miles per hour.

Arden then took a van tour of the chapels in the city. The van traveled at an average of 10 miles per hour and covered 50 miles. The van then returned Arden to a Tube station, where he traveled 15 minutes by Tube to his hotel. He returned to his hotel 9 hours and 15 minutes after boarding the double-decker bus.

In the table below, indicate how much of Arden’s journey was spent traveling by bus, and indicate the amount of time Arden spent exploring specific locations of interest during his tour of the London area. Make only two selections, one in each column.

Let's break down the information:

Para 1:

Arden spent his vacation touring London and Paris. On his first day in London, he boarded a double-decker bus, which traveled 30 miles through the city at an average speed of 15 miles per hour. He then boarded a tour bus and traveled 30 miles outside the city. The bus stopped at a museum outside of London for lunch for 60 minutes before returning to its original location in the city. The bus traveled an average of 60 miles per hour.

- Time on double decker bus (30 miles at 15 miles/hour) ie., 2 hours
- Time on tour bus (60 miles in total for the onward and return journey at 60 miles/hour) ie., 1 hour (30 minutes onward and 30 minutes return)
- Time spent at museum Outside London for lunch - 1 hour

Great - so far, from para 1, we see we have 4 hours of travel that Arden covered.

Para 2:

Arden then took a van tour of the chapels in the city. The van traveled at an average of 10 miles per hour and covered 50 miles. The van then returned Arden to a Tube station, where he traveled 15 minutes by Tube to his hotel. He returned to his hotel 9 hours and 15 minutes after boarding the double-decker bus.

Time spent in Van of Chapels IN the city (50 miles at 10 miles/hour) ie., 5 hours
Time spent on Tube to go to hotel - 15 minutes

Hence total time was 9 hours and 15 minutes as mentioned in last line.

Let's answer the questions


Q1 Time Spent Traveling By Bus

Time spent on double decker and tour bus - 2+1 = 3 HOURS

Q2 Time Spent Exploring Locations of Interest

Trick one.. Let's look at each segment of trip

Double decker bus - yes, counts - so 2 hours
Tour bus - does not count as 'exploring'
Museum - it is outside London but question asks "time Arden spent exploring specific locations of interest during his tour of the London area", we can count this - 1 hour
Van tour - yes counts - 5 hours

Here I got 8 hours, so I chose to eliminate Double decker bus as it might not count as 'exploring'

Hence 6 HOURS
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Time Spent Traveling By Bus
Arden boarded a double-decker bus, which traveled 30 miles through the city at an average speed of 15 miles per hour
=> he travelled in bus for 2 hours.

He then boarded a tour bus and traveled 30 miles outside the city.
The bus stopped at a museum outside of London for lunch for 60 minutes before returning to its original location (30 miles) in the city. The bus traveled an average of 60 miles per hour.
=> he travelled in bus for 1 hour.
Thus, the time spent by him travelling by Bus is 3 hours.

Time Spent Exploring Locations of Interest
Arden boarded a tour bus which took him to a Museum outside the city. He spent 1 hour there.
Also, he took a van tour of the chapels in the city. The van traveled at an average of 10 miles per hour and covered 50 miles.
=> he spent 5 hours in the Van exploring locations of interest.
Total time spent by him = 6 hours.
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Time spent in the double decker bus to travel through city= 2 hours ( 30 miles/ 15 miles per hour)
Distance Traveled by tour bus 60 miles ( 30 miles each for going and returning to the museum)
Time Spent in bus travel for visit to museum = 1 hour ( 60 miles/ 60 miles per hour)
Time spent on lunch= 1 hour
Time travel in Van for chapel visits= 5 hour (50 miles/ 10 miles per hour)
Time travel in tube= 15 minutes

Total time spent till returning to hotel= 9 hour 15 minutes.

Total Time spent travelling by bus= 3 hours
Time spent in tour bus+ Time spent in double decker bus = 1hour +2 hours= 3 hours

Time Spent Exploring Locations of Interest= 6 hour
Time travel in Van for chapel visits + Time Spent in bus travel for visit to museum= 5 hours + 1 hours = 6 hours
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given : Arden returned to his hotel 9 hours and 15 minutes after boarding the double-decker bus.

time for double-decker(dd) bus = 30/15 = 2hrs
distance travelled in tour bus = 30miles(going away from city) + 30miles(coming back to city) = 60miles
time for tour bus = 60/60 = 1hr
lunch time = 1hr
time for van tour = 50/10= 5hrs
walking time = 15mins

Time Spent Traveling By Bus = time for double-decker(dd) bus + time for tour bus = 2hrs+1hr = 3hrs
Time Spent Exploring Locations of Interest = time for tour bus + time for van tour = 1hr+5hrs = 6hrs
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Arden spent his vacation touring London and Paris. On his first day in London, he boarded a double-decker bus, which traveled 30 miles through the city at an average speed of 15 miles per hour. He then boarded a tour bus and traveled 30 miles outside the city. The bus stopped at a museum outside of London for lunch for 60 minutes before returning to its original location in the city. The bus traveled an average of 60 miles per hour.

Arden then took a van tour of the chapels in the city. The van traveled at an average of 10 miles per hour and covered 50 miles. The van then returned Arden to a Tube station, where he traveled 15 minutes by Tube to his hotel. He returned to his hotel 9 hours and 15 minutes after boarding the double-decker bus.


In the table below, indicate how much of Arden’s journey was spent traveling by bus, and indicate the amount of time Arden spent exploring specific locations of interest during his tour of the London area. Make only two selections, one in each column.

For Arden's journey (in simple terms) :-

DD Bus -- 30 miles ---15 mph --2 hrs (Inside City travel)
Tour Bus -- 60 miles (30 miles (to) & 30 miles (fro)) ---60 mph --1 hrs (Outside City..Tour)
Lunch Halt ------------------------------------------------------------- 1 hr
Van Tour -- 50 miles ---10 mph --5 hrs (Outside City..Tour)
by Tube ----------------------------------------------------------------- 1/4 hrs

-------------------------------------------------------------------------------------
Total Time taken - 9 1/4 hrs
-------------------------------------------------------------------------------------

QUESTION 1

Time Spent Traveling By Bus


Bus Travel = 2 hrs + 1 hrs = 3 hrs

(3 hours, 0 minutes) is the CORRECT answer


QUESTION 2

Time Spent Exploring Locations of Interest (Tour)


Bus Travel = 1 hrs + 5 hrs = 6 hrs

(6 hours, 0 minutes) is the CORRECT answer
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(A) Time Spent Traveling By Bus

Arden spent his vacation

travelling by Double Decker Bus = 2 hour (ie, 30 miles through the city at an average speed of 15 miles per hour)
travelling by Tour Bus = 1 hour (ie, 60 miles (30+30) through the city at an average speed of 60 miles per hour)

Total Time = 3 hour

(A) Time Spent Traveling By Bus = 3 Hours 0 Minutes


(B)Time Spent Exploring Locations of Interest

Arden spent his vacation

travelling by Tour Bus (outside City) outside City = 1 hour (ie, 60 miles (30+30) through the city at an average speed of 60 miles per hour)
Van tour of the Chapels = 5 hours (ie, 50 miles at an average speed of 10 miles per hour)

Total Time = 6 hours

(A) Time Spent Exploring Locations of Interest = 6 Hours 0 Minutes
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The official answer to the question is posted, it is:

Time Spent Traveling By Bus: 3 hours, 0 minutes
Time Spent Exploring Locations of Interest: 6 hours, 0 minutes

Competition mode is off now.
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Official Explanation

Arden traveled by bus twice during the day. The first time was on a double-decker bus in the city. The bus traveled for 30 miles at 15 miles per hour, so Arden spent 2 hours on this bus. The second bus was a tour bus outside the city. The tour bus traveled 60 miles round trip at 60 miles per hour, so Arden spent 1 hour on this bus. He spent 3 hours total on the two buses.

Arden explored locations of interest twice: the museum outside of London and chapels within London. He spent 60 minutes at the museum and toured chapels for 50 miles. The chapel van traveled 10 miles per hour, so the chapel tour took 50 ÷ 10, or 5 hours. Altogether, Arden spent 6 hours exploring locations of interest.

Answer:
Time Spent Traveling By Bus: 3 hours, 0 minutes
Time Spent Exploring Locations of Interest: 6 hours, 0 minutes
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