SOLUTION: Ivan drives to the metro station each morning and just to catch his train. He drives at an average speed of 30 miles per hour. Unfortunately this morning, there was a lot of traffi

Question 1005182: Ivan drives to the metro station each morning and just to catch his train. He drives at an average speed of 30 miles per hour. Unfortunately this morning, there was a lot of traffic. At the halfway point Ivan found that he had averaged only 15 miles per hour. How fast must Ivan drive for the rest of the way to catch his train?
Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
suppose the distance is 60 miles; it takes him 2 hours.
After 30 miles, half way, averaging 15 mph, he has already been traveling 2 hours.
He can't make the train.
Let x=distance
normal distance is 30 mph*time=x
normal time is x/30, units miles/miles/hour or hours
half way through, or x/2 miles, has taken him x/(2*15) hours. But that is x/30 hours, so he can't make the train.

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Key phrase, "at the half-way point".

How fast needs to drive, r.

Regular 30 () d First half 15 () d/2 Next half r () d/2

Fill in the missing time expressions.

Regular 30 (d/30) d First half 15 d/(2*15) d/2 Next half r d/(2r) d/2

Ivan will be late, and can NOT catch the train. He used up all the needed travel time at the half-way point of the trip.
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