Alice and bob are running a race. alice and bob run at constant speeds. since bob is slower than alice, he gets a head start. he starts the race running at 8 miles per hour. some time later, alice starts running at 10 miles per hour. alice passes bob a mile from the starting line. in minutes, how much time was bob's head start? express your answer as a decimal to the nearest tenth.

0.02 hours

Step-by-step explanation:

Given that they have contant speeds.

Let the speed of alice be v1 and that of bob be v2.

Given that v2=8 miles per hour

v1=10 miles per hour

It is given that alice crosses bob at a distance of 1 mile.

Time taken for alice to go 1 mile is 0.1 hours.

Distrance travelled by bob in this time is 0.8 miles.

So bob will have crosses 0.2 miles by the time alice starts running.

So head start of bob would be hours i.e.0.025 hours.

Decimal to the nearest tenth is 0.02 hours.

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.