A car passes a landmark on a highway traveling at a constant rate of 40 kilometers per hour. Two hours later, a second car passe
s the same landmark traveling in the same direction at 65 kilometers per hour. How much time after the second car passes the landmark will it overtake the first car? Do not do any rounding.
So first you want to find how much the second car gains on the first car in one hour.
Since the second car travels 65 kph, but the first travels 40, we can just subtract 40 from 65 to find how much faster the second car is than the first.
65 - 40 = 25
So the second car is 25 kph faster than the first.
Since the first car had a 2 hour head start, we first want to calculate how far away the first car got from the sign before the second car reached the sign.
So just 2 hours * 40 kph, which gives you 80 kilometers.
So now we know the second car has to gain 80 km on the first car in order to overtake it.
Since the second car gains 25 km per hour on the first car, we can just divide 80 by 25.
80 / 25 = 16/5, or in decimal form 3.2.
So the second car will overtake the first car in 3.2 hours, or 192 minutes, which is also 3 hours and 12 minutes.
To find the LCM of two numbers, first find the prime factorization of each number. Then the LCM is the product of common and not common factors with the larger exponent.
