Question

Two truckers leave from the same point driving in opposite​ directions, the first trucker driving at 62 miles per hour and the second at 66 mph. The first trucker has a​ one-hour head start. How​ long, after the first trucker​ leaves, will they be able to contact each other on their car phones if the phones have a 270​-mile ​range?

Answer 1

Answer:

1 hour 42 minutes

Step-by-step explanation:

Given: Speed of 1st trucker= 62 mph

           Speed of 2nd trucker= 66 mph

           Total distance need to cover to be in contact is 270 miles

           1st trucker start 1 hour ahead of 2nd trucker

Lets assume 2nd trucker take `x` hours to be in contact and 1st trucker take `(x+1)` hours.

We know, distance= $speed\times time$

1st trucker, distance$(d_1)= 62\times (x+1)$

                     ∴ $d_1= 62x+62$

2nd trucker, distance$(d_2)= 66\times x$

                    ∴$d_2= 66x$

Now, putting the values in an equation.

$d_1+d_2= 270$

⇒ $(62x+62)+66x= 270$

Opening the parenthesis to solve and subtracting both side by 62

⇒ $122x= 208$

∴ x= $\frac{208}{122} = 1.70\ h$ = 1 hour 42 minutes

∴ It will take 1 hour 42 minutes to be able contact each other after first trucker leaves.