I need to come up with an equation to answer the following: Julia drives the 120

Question

I need to come up with an equation to answer the following: Julia drives the 120 miles from Greenup to Goldberg at 46 mi/hr, while Beth drives from Goldberg to Greenup at 34 mi/hr. How long will it take for Julia and Beth to meet each other if they leave their respective locations at the same time? I need to come up with an equation to answer the following: Julia drives the 120 miles from Greenup to Goldberg at 46 mi/hr, while Beth drives from Goldberg to Greenup at 34 mi/hr. How long will it take for Julia and Beth to meet each other if they leave their respective locations at the same time?

Explanation / Answer

given that they leave their respective locations at same time

Let speed of Julia be U1 and speed of Beth be U2

Distance between both the cities be D

where D=120 miles

U1 = 46mi/hr , U2 = 34 mi/hr

let us assume that they meet each ther at a distance x from Greenup at time t

So here we equate the times taken for julia and Beth to meet

so since t= d/u

we have x/U1 = (D-x)/U2

   xU2 = DU1 - xU1

   x(U1+U2) = DU1

   x= DU1/(U1+U2)

   x = 120*46/(46+34) = 120*46/80 = 69 miles

   so time taken for meeting = x/U1 = 69/46 = 1.5 hours

   t = 1.5 hr

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