What time did the Garcias overtake the Smiths?

Question

At 8 AM the Smiths left a campground, driving at 48 mph. At 8:20 AM, the Garcias left the same campground and followed the same route, driving at 60 mph. At what time did they overtake the Smiths?

Answer 1

60 t = 48 (t + 1/3)    the Smiths had a 20 min head start

12 t = 16 ___ t = 4/3 or 1:20

8:20 + 1:20 = 9:40

 

they overtook when they have travelled the same Distance (rate x time)

Answer 2

at the time the cars meet, they will have driven the same distance. Right?

 

so we know the distances are the same.

 

the basic formula is distance = speed x time which your teacher must have given you because otherwise it is impossible to answer a question such as this.

 

so for the Smith's, let us call the total driving time t in hours

the Garcia's left 20 minutes later so we have to subtract that much from the time for the Smith's. First change to hours.

 

20 minutes = 1/3 hour

 

so the time for the Garcia's is (t - 1/3)

 

the speed's are given so we know those

 

now we can use the formula

 

Smith distance = 48mph x t

Garcia distance = 60mph x (t - 1/3)

 

Remember we said the distances are the same

 

48t = 60(t - 1/3)

 

48t = 60t - 20

 

12t = 20

 

t = 1 2/3 hours = 1 hour 40 minutes is the time traveled by the Smith's who left at 8AM

 

So the answer is 9:40 AM