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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?

Respuesta :

caleb drove fast cause he went faster

Answer:

Caleb arrived earlier.

Also, he arrived 2 hours earlier.

Step-by-step explanation:

We know that,

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

For Alyssa,

Distance = 105 miles,

Time = 3.5 hours,

∴ Alyssa's speed = [tex]\frac{105}{3.5}[/tex] = 30 miles per hour,

For Caleb,

Distance = 168 miles,

Time = 4 hours,

∴ Caleb's speed = [tex]\frac{168}{4}[/tex] = 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 = [tex]\frac{210}{42}[/tex] = 5 hours,

While, the time taken by Alyssa in the entire journey = [tex]\frac{210}{30}[/tex] = 7 hours,

∵ 7 - 2 = 5

Hence, Caleb arrived 2 hours earlier.

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