Question

Cyclists A and B rode along a straight one way road starting from the same location and they rode for one hour. Cyclist A rode half the time with speed 10miles/hour and the other half time with speed 30 miles/hour. Cyclist B rode half the total distance with speed 10 miles/hour and half the distance with speed 30/hours.

Calculate the total distance traveled by cyclist B. Calculate the average velocity for cyclist B.

Answer 1

did cyclist A and B ride the same amount of distance?

Answer 2

i don't think so.

Answer 3

then why is cyclist A mentioned at all?

Answer 4

cause i thought you might need the information, so I put it there just in case. Sorry.

Answer 5

is there any other part of the question that asks you about cyclist A? because then it would be unnecessary information which math questions rarely do unless you have a douchebag teacher.

Answer 6

yeah I think it was just uneccesary info for A. Any help on solving this question for cyclist B?

Answer 7

yeah actually you dont need other information at all. my bad, wasn't thinking straight. now that i wrote it all down, it makes sense

Answer 8

ok what we first start is that lets declare variables.

Answer 9

first: distance. lets call the distance of this whole road D.

Answer 10

second: the time. cyclist B traveled 10mph for half of the distance (1/2 * D) and 30mph for half of the distance (1/2 * D)

Answer 11

the time cyclist B traveled 10 mph = X
the time cyclist B traveled 30 mph = Y

Answer 12

since distance = time * velocity
1/2 * D = X * 10
1/2 * D = Y * 30

Answer 13

thus, we see that 10*X = 30*Y
meaning being, X = 3Y

Answer 14

in the question, it said that the cyclists traveled for an hour
thus we know that X + Y = 1

Answer 15

now it's piece of cake. first we find X and Y.
since X = 3Y, we can substitute that into X+Y = 1 which will become Y + 3Y = 1

Answer 16

Y = 0.25 (hours) = 15 minutes.
X = 45 minutes.
the cyclist traveled 10mph for 45 minutes and 30mph for 15 minutes.

Answer 17

now we find the D (distance). 10 mph * 3/4 hours + 30 mph * 1/4 hours = D

Answer 18

total distance is then 15 miles I believe. that's the answer to the first part of the question.

Answer 19

second part is the average velocity. average velocity is calculated by the total distance traveled divided by the time it took.

Answer 20

15 miles / 1 hour. thus the average velocity is 15 mph.

Answer 21

this could be a tricky question because you went half-way as 30mph and half-way as 10mph. so you could think that the average velocity is 20mph (as average of 30 and 20), but math tells otherwise. so its just best to do step by step like this.

Answer 22

any question?