At 3 p.m., Brunhilde headed north at 30 kilometers per hour. Two hours later Ludwig headed south at 40 kilometers per hour. At what time will they be 340 kilometers apart?

Question

I know that the distance from Brunhilde(Db) plus the distance from Ludwig(Dl) is equal to 340, which is translated as (Tb)(Rb)+(Tl)(Rl)=340, "T" standing for time, and "R" standing for rate...so I substitue in the rates to get 40Tb + 30Tl=340, but the answer is wrong..the book has it as 9 p.m....what am I doing wrong!!!!?

Answer 1

They separate at a rate of 30 + 40 =
70 km/hr, since they are going in opposite directions. It takes 340/70 = 4.857 hours to become 340 km apart. That would be at 8:51 PM, since 0.857 x 60 = 51+ minutes. Are you sure they didn't ask for the time when they are 350 km apart, not 340? Then the answer would be exactly 9 PM

Answer 2

Yea the answer in the back of the book has it at 9 p.m. ,and yea they do ask for the time when their 340 kilometers apart, interesting, could the book be wrong?lol

Answer 3

When you divided 340/70 and came up with 4.857, how'd you come up with 8?

Answer 4

The book is correct.

Let the time passed after Ludwig left be t hours, remember he left 2hours after her, so she already went 60 km

So the distance that Brunhilde went is 60+30t
and the distance that Ludwig went is 40t
so....
60 + 30t + 40t = 340
70t = 280
t = 4

So they are 340 km apart 4 hours after Ludwig left, but he left at 5 pm, so they are apart 340 km at 9 pm

Answer 5

Sorry; I misread the problem and neglected the time delay

Answer 6

I think it's wrong, I’m currently doing this math book and I keep coming up with 8:00pm.