Find the average speed

[Anna55]

When Amanda goes to work she has the average speed 90km/h. On the way home her average speed is only 30 km/h. Which is her average speed for the whole journey to and back from work?

 

[tkhunny]

Average Speed = Total Distance / Total Time

Since we know neither, we're done.

RBGTHGANH

 

[tkhunny]

jk - Now that i am awake, let's try this again.

DistanceTo = SpeedTo * TimeTo

DistanceFrom = SpeedFrom * TimeFrom

We know SpeedTo = 90 kmh and Speedfrom = 30 kmh

DistanceTo = 90 kmh * TimeTo

DistanceFrom = 30 kmh * TimeFrom

A moment's thougth suggests DistanceTo = DistanceFrom

DistanceTo = 90 kmh * TimeTo

DistanceTo = 30 kmh * TimeFrom

90 kmh * TimeTo = 30 kmh * TimeFrom

A little more thought suggests TimeFrom = 3*TimeTo

90 kmh * TimeTo = 30 kmh * 3*TimeTo

A little algebra

90 kmh * TimeTo = 90 kmh * TimeTo -- Well, that doesn't get us anywhere, but it was worth the exploration.

 

[TchrWill]

When Amanda goes to work she has the average speed 90km/h. On the way home her average speed is only 30 km/h. Which is her average speed for the whole journey to and back from work?

Let D = the distance to work, T1 = the time to work, T2 = the return time and T = the total time.
Remember that average speed for an entire trip is the "total" distance traveled divided by the "total" time for the trip.
T1 = D/90 and T2 = T/30
Total time to and from work = T = D/90 + D/30 = 120D/2700
Average speed for the whole journey = Va = 2D/(120D/2700) = 45km/hr.

 

[Anna55]

Thank you TchrWill! I understand it now.

 

[tkhunny]

If you would show ANY work at all, I wouldn't badger you.