At 4PM Charlie realized he has half an hour to get to his grandmothers house for dinner. If his grandmother lives 40 miles away, how fast will Charlie have to drive to get there on time

40 mph

Step-by-step explanation:

So, Charlie has 30 minutes (or 1/2 hour) to ride 40 miles by car. So, he needs to go at a speed such that he can make 40 miles in 1/2 hour.

Lets X miles per hour be the needed speed to ride 40 miles in half an hour, we know that at such speed Charlie will ride X miles in 1 hour. As the time he has is 1/2 hour we need X to be 80. This is, at a speed of 80 miles per hour, Charlie will ride 40 milles in half an hour. Note that:

80/40 = 1 / (1/2) are proportionals