Question 872665
{{{x}}}= his present speed, in mi/h
{{{x+10}}}= a speed (in mi/h) 10 mi/h faster than his present speed
{{{3(x+10)}}}= distance he would travel in 3 hours, driving 10 mi/h faster than his present speed
{{{4x}}}= distance he would travel in 4 hours, driving at his present speed
The problem says that {{{3(x+10)}}} is a greater distance than {{{4x}}} .
We write that as
{{{highlight(3(x+10)>4x)}}}
 
NOTE:
The part above answers "write an inequality based on the given information, do not solve."
If you want to know how to solve that inequality, here it goes
{{{3(x+10)>4x}}}
{{{3*x+3*10>4x}}}
{{{3x+30>4x}}}
{{{30>4x-3x}}}
{{{30>x}}} or {{{x<30}}}
Reality check:
Does it make sense?
If he was driving at 30 mi/h, in 4 hours he would travel
(30 mi/h)(4 h) = 120 mi
Going 10 mi/h faster, at 30 mi/h + 10 mi/h = 40 mi/h,
in 3 hours he would travel the same distance
(40 mi/h)(3 h) = 120 mi.
However, if he is driving slower, for example at 29 mi/h,
in 4 hours he would travel
(29 mi/h)(4 h) = 116 mi.
Going 10 mi/h faster, at 29 mi/h + 10 mi/h = 39 mi/h,
in 3 hours, the distance he would travel is
(39 mi/h)(3 h) = 117 mi,
so driving 10 mi/h faster, he would indeed travel farther in 3 h.
The conclusion is
if you are driving slow, increasing your speed by 10 miles per hour would help.
If you are already going at a good speed, you do not gain that much by driving 10 miles per hour faster.
We sort of knew that, didn't we?