# Seth drove from Lancaster to Philadelphia at an average speed of 64. By traveling at an average speed of 78 miles per hour he could have arrived 10 minutes earlier. How far is it from Lancaster to Philadelphia?

Mar 9, 2018

59.43 miles

#### Explanation:

Let the distance between Lancaster to Philadelphia is x miles.

Seth goes 64 miles in 1 hour. So he goes x miles in x/64 hour.

Again if he goes 78 miles in 1 hour. Then it took x/78 hours.

Now, as per question he saves 10 minutes = 10/60 = 1/6 hours.

So, $\frac{x}{64} - \frac{x}{78} = \frac{1}{6}$
$\Rightarrow \frac{39 x - 32 x}{2.32 .39} = \frac{1}{6}$
$\Rightarrow \frac{7 x}{2.32 .39} = \frac{1}{6}$
$\Rightarrow x = \frac{1.2 .32 .39}{6.7}$
$\Rightarrow x = 59.43$

[Note : L.C.M. of 64,78 is 2.32.39]