Question

Alyssa and Caleb drove 210 mikes to the beach in separate cars. They left at the same time. They both drove at a constant speed. Alyssa drove 105 miles in 3.5 hours. Caleb drove 168 miles in 4 hours. Who arrived earlier? How much earlier?

Answer 1

caleb drove fast cause he went faster

Answer 2

Caleb arrived earlier.

Also, he arrived 2 hours earlier.

Explanation:

We know that,

`Speed = (Distance)/(Time)`

For Alyssa,

Distance = 105 miles,

Time = 3.5 hours,

∴ Alyssa's speed =
`(105)/(3.5)` = 30 miles per hour,

For Caleb,

Distance = 168 miles,

Time = 4 hours,

∴ Caleb's speed =
`(168)/(4)` = 42 miles per hour,

Since, they are driving with the constant speed,

Thus, Caleb's speed > Alyssa's speed

That is, Caleb will arrive earlier, ( Time ∝ 1 / speed )

Now, they both have to cover 210 miles,

Time taken by Caleb in the entire journey =
`(210)/(42)` = 5 hours,

While, the time taken by Alyssa in the entire journey =
`(210)/(30)` = 7 hours,

∵ 7 - 2 = 5

Hence, Caleb arrived 2 hours earlier.