Question

William traveled by scooter at an average speed of 62 miles per hour. Then, he traveled by car at an average speed of 36 miles per hour. In total he traveled 118 miles for 2 hours. How many minutes did William travel by car? ( Round to the nearest minute)

Answer 1

distance = rate * time (ds=distance on scooter) (dc=distance on car)
--------------------
ds = rs * ts
dc = rc * tc

(rc is rate of car; rs is rate of scooter; ts is time on scooter; tc is time on car)

Answer 2

we already know rs and rc

Answer 3

yes

Answer 4

ds = 62 * ts
dc = 36 * tc

dt = total distance = 118 =62 * ts + 36 * tc
tt = total time = 2 = ts + tc

Answer 5

these are all of the equations we need, do you know how to solve for ts and tc. We have 2 equations and 2 unknowns at this point

Answer 6

Wait, let me try.

Answer 7

oh, also remember to convert hours to minutes once you have solved for tc

Answer 8

ok

Answer 9

can you show me the steps. Im kind of stuck

Answer 10

118 = 62 * ts + 36 * tc
2 = ts + tc

we will use substitution

Answer 11

ts = 2-tc

Answer 12

ok

Answer 13

substitute (2-tc) wherever there is a ts in the following equation
118 = 62 * ts + 36 * tc

becomes

118 = 62 * (2-tc) + 36 * tc

Answer 14

can you solve this equation?

Answer 15

not really

Answer 16

start by distributing the 62 into the (2 - tc)

Answer 17

124-62*ts

Answer 18

i mean 124 - 62*tc

Answer 19

124-26tc

Answer 20

now put the rest of the equation around what you got

Answer 21

-6 - 26tc

Answer 22

118 = 124 - 26*tc + 36*tc

Next step is to combine like terms

Answer 23

oops my equation is wrong

Answer 24

Yea i Was about to say that

Answer 25

118 = 124 - 62*tc + 36*tc

Answer 26

i think you just left out an equal sign

Answer 27

Yea

Answer 28

-6= -26tc

Answer 29

Solve for tc. just remember to convert your answer to tc, which is in hours, into units of minutes (which is what the problem asks for).

Answer 30

ok

Answer 31

i got 0.230769 repeating...

Answer 32

Can you help me out?

Answer 33

that fine, this number is in hours. we are interested in calculating the number of minutes spent in the car. Therefore, we need to convert hours to minutes.

Answer 34

ok

Answer 35

so we do 60/5

Answer 36

and get 14 minutes?

Answer 37

\[\frac{number of hours}{1}*\frac{60 minutes}{1hour}=numberofminutes\]

Answer 38

your answer seems right

Answer 39

Yes! Thank You!

Answer 40

great!