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## Comment on

Cole’s Travel Time## Hey, IF we can take 2-W for

## That's correct

That's correct

## Hey ... If I use the first

## Sure thing.

Sure thing.

time = distance/speed

Let d = distance EACH way.

Speed going TO work is 75 kmh.

So, time to get to work = d/75

Speed going FROM work is 105 kmh.

So, time to get home = d/105

(time to get to work) + (time to get home) = 2 hours

d/75 + d/105 = 2

Solve for d to get d = 87.5 km

We already know that time to get to work = d/75

So, time = 87.5/75

= 175/150

= 1 25/150

= 1 1/6 hours

= 70 minutes

= B

## Could you please show how you

## You bet.

You bet.

We have: d/75 + d/105 = 2

To eliminate the fractions, multiply both sides of the equation by the least common multiple of the denominators 75 and 105

So, multiply both sides of the equation by 525 to get: 7d + 5d = 1050

Simplify: 12d = 1050

Solve: d = 87.5

## Could you please show how

## You bet.

You bet.

How's this: 175/150 = (150 + 25)/150

= 150/150 + 25/150

= 1 + 25/150

= 1 + 5/30

= 1 + 1/6

= 1 1/6 hours

= 1 hour + (1/6 of an hour)

= 60 minutes + 10 minutes

= 70 minutes

## Sir i solved this Question

we have the formula for Avg speed = (d+d)/(t1+t2).

t1 = time taken to travel from home to office

t2 = time taken to travel from office to work.

for t1= d/75

for t2= d/105

as we know t1+t2 = 2

therefore

d/75 + d/105 = 2

after taking lcm we get

105d+75d =15750

180d = 15750

d=87.5km

therefore t1=d/75 = 87.5/75 = 1.167hours =>1.167x60min we get 70min

therefore 70min is the answer

## Another valid approach. Great

Another valid approach. Great work!

## Hi Brent,

Awesome videos. As explained, these problems can be solved in multiple ways. What I am having trouble with is deciding on which method will produce the answer quickest. Would appreciate your thoughts. Cheers.

## Great question!

Great question!

In order to determine which approach will yield the quickest answer, you need to roughly predict the number of steps each approach will take.

For example, if a certain word problem can be solved algebraically or by testing the answer choices, you need to predict how long it will take you to create and solve the equations in an algebraic solution and compare that to how long it will take you to test each answer choice.

Cheers,

Brent

## hey Brent! I got tripped up

## I'd say the most relevant

I'd say the most relevant piece of information is that the question doesn't ask us to find the average speed; it asks us to find the time it takes Cole to get to work.

Aside: When we're given "average speeds" in a question like this, you can pretty much ignore the word "average" and just assume that the given people/vehicles are travelling at constant speeds.

## Is it generally better to use

## That's 100% correct. Since we

That's 100% correct. Since we want to find TIME, we should NOT use the equation where we compare TIMES.

That said, if we DO use the equation that compares times, we'll just have one small extra step to answer the question.