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Patty and Toby live 345 miles apart. They decide to drive to meet one another. Patty leaves at noon, traveling at an average of 45 mi/h , and Toby leaves at 3:00 pm , traveling at an average speed of 60 mi/h . At what time will they meet?

Answer :

Answer:

They will meet at 5:00 PM

Step-by-step explanation:

[tex]Speed =\frac{Distance}{Time}[/tex]

[tex]\implies Distance = Speed\times time[/tex]

Let Patty takes t hours to meet Toby,

Patty's speed = 60 miles/h

So, the distance covered by Patty = 60t miles,

Patty leaves at noon and Toby leaves at 3:00 pm with speed of 60 mi/h,

So, the time taken by Toby = (t-3) hours,

Thus, the distance covered by Toby = 60(t-3) miles

When they meet,

Distance covered by patty + Distance covered by Toby = total distance them

[tex]45t + 60(t-3) = 345[/tex]

[tex]105t - 180 = 345[/tex]

[tex]105t = 525[/tex]

[tex]t=\frac{525}{105}=5 [/tex]

Hence, they meet 5 hours after 12:00 PM i.e. 5:00 PM.

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