16 Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from either one or two riders at a time. Regardless of the number of people school each day: cycle on a tandem bike or walk. The bike can carry pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour. a On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Reeta when the cyclists arrive home? b On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back towards school to collect Nikita. How far from school is Nikita when Reeta reaches her? c On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta hops off and walks the rest of the way, while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike? off at a
16 Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from either one or two riders at a time. Regardless of the number of people school each day: cycle on a tandem bike or walk. The bike can carry pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour. a On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Reeta when the cyclists arrive home? b On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back towards school to collect Nikita. How far from school is Nikita when Reeta reaches her? c On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta hops off and walks the rest of the way, while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike? off at a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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16 Tandem Cycling
Triplets Peter, Reeta and Nikita have two ways for getting home from
school each day: cycle on a tandem bike or walk. The bike can carry
either one or two riders at a time. Regardless of the number of people
pedalling, cycling speed is 5 times walking speed. The triplets always
leave school at the same time and always use the same path between
school and home, whether walking or cycling. The school is 5 km from
home and their walking speed is 4 kilometres per hour.
a On Monday, Nikita and Peter cycle and Reeta walks. On reaching the
point four-fifths of the way home the bike gets a puncture, so Nikita
and Peter walk the rest of the way home. How far from school is
Reeta when the cyclists arrive home?
b On Tuesday, Peter and Reeta ride the bike and Nikita walks. When
the cyclists arrive home, Peter hops off the bike and Reeta rides back
towards school to collect Nikita. How far from school is Nikita when
Reeta reaches her?
c On Wednesday, Reeta and Nikita take the bike and Peter walks. When
the cyclists are halfway home, Reeta hops off and walks the rest of the
way, while Nikita heads back to pick up Peter. How far from school
is Reeta when her siblings pass her on the bike?
d On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a
certain point leaving her to walk home. Meanwhile he returns to pick
up Reeta and they cycle home together. If all three arrive home at the
same time, how far from school are the drop-off and pick-up points?
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