I need help on these 2 math problems, please!

Question

1)) (write and equation) 

A truck leaves a house and travels at a steady rate of 40mi/h. the family leaves the house 1 hour later following the same route. they travel at a steady rate of 60mi/h. How long after the moving truck leaves rhe house will the car catch up with he truck?

 

 

2)) an insurence company salesperson earns a salary of $4,200 per month plus a commision of 3% of sales. how much must the salesperson sell to have a monthly income of at least $4,500? 

 

thank you so much!

 

Answer 1

1) to solve the first question, you need to know the greatest common multiples of both speeds; Moving Truck  = 40mph and Family Car = 60 mph.

MT) 40 - 80 - 120 - 160 - 200

FC) 60 - 120 - 160 - 200

 

Next, if the family car left a hour after the moving truck, then we know the following:

In 1 hour, the moving truck has traveled 40 miles (40mph * 1 hours) and the family car has traveled 0 miles, because they hadn't left yet (60mph * (1 hour -1 hour delay)).

After 2 hours,  the moving truck has traveled 80 miles (40mph * 2 hours) and the family car has traveled 60 miles (60mph * (2 hours -1 hour delay)).

After 3 hours, the moving truck has traveled 120 miles (40mph * 3 hours) and the family car has traveled 120 miles (60mph * (3 hours -1 hour delay)).

The formula to solve this problem would be expressed algebraically as: x = hours traveled 40mph*x=60mph*(x-1)

 

2) So, what we know is that a salesperson makes $4200 a month and 3% commission on sales. Commission is what part of the salesperson's total sales they get. The question wants us to find out how much total sales the salesperson had in order to receive a total monthly salary of $4500. So X = the total amount of sales the salesperson had in a month

so, algebraically, this problem would be expressed as: $4200+0.03X=$4500. Instead of writing the 3% out as a percentage, I wrote it as a decimal. This is important in order to get the correct answer. Now you just reduce the problem to isolate X. First, subtract $4200 from both sides of the equation to get 0.03X=$300. Next, divide both sides by 0.03 to isolate X. You get X = $10,000.

 

Answer 2

1. Distance = rate*time

truck: rate=40 time=x

car: rate=60 time=x-1 (because the car left one hour after the truck, so the car will travel one less hour when it catches up)

Using the distance = rate*time formula, the distance the truck travels can be represented by:

d=40*x

The distance the car travels can be represented by:

d=60(x-1)

Since the car has to catch up with the truck, at that moment they will

have covered the same distance

so their distances are equal. 

So you can set their distance equations equal to each other:

40x=60(x-1)

then solve for x. 

40x=60x-60

-20x=-60

x=3

so the car catches up to the truck at 3 hours after the truck first started.