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melomori [17]
3 years ago
13

A truck left the station at 6 a.m. traveling at a rate of 45 km/h. A van left the same place 2 hours later heading in the same d

irection at a rate of 54 km/h. At what time will the van catch up with the truck?
Mathematics
1 answer:
Ghella [55]3 years ago
8 0

Answer:

6 PM

Step-by-step explanation:

The truck has a 2 hour head start.  It is moving at 45 km/h, so it is 90 km ahead.

If t is the time after 8 AM, then the distance between the truck and the station is:

d = 90 + 45t

The distance between the van and the station is:

d = 54t

When the distances are equal:

54t = 90 + 45t

9t = 90

t = 10

It takes 10 hours after 8 AM for the van to catch up with the truck.  So the time would be 6 PM.

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What is 6-2p=p+9 ?Because I don't know it​
nikklg [1K]

Hey there!

  • Firstly, you have to \bold{simplify} each of the sides of your equation
  • \bold{6-2p-p+9\downarrow}
  • \bold{6+(-2p)=p+9\downarrow}
  • \rightarrow\bold{-2p+6=p+9}
  • Now that you have that  portion out of the way, we could  move on to our second step... which is to \bold{subtract} by the value of  \bold{p} on each of your sides
  • \bold{-2p+6-p-p+9-p\downarrow}
  • \rightarrow\bold{-3p+6-9} (you get this because we solve the particular equation we added above)
  • Thirdly, you have to \bold{subtract} by the number \bold{6} on each of your sides
  • \bold{-3p+6-6=9-6\downarrow}
  • \bold{Cancel:6-6} because it equals to \bold{0}
  • \bold{Keep:9-6} because it brings us closer and closer to the answer of \bold{p}
  • Fourthly, we have to \bold{divide} by  the number \bold{-3} on each of your sides
  • \bold{\frac{-3p}{-3}=\frac{3}{-3}}
  • \boxed{\boxed{\bold{Answer:p=-1}}} \checkmark

Good luck on your assignment and enjoy your day!

~\frak{LoveYourselfFirst:)}

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