Algebra problems?

Question

1. A postal truck leaves its station and heads for Chicago, averaging 40 mph. An error in the mailing schedule is spotted and 24 minutes after the truck leaves, a car is sent to overtake the truck. If the car averages 50 mpg, how long will it take to catch the postal truck?

2. In the Klysler Auto Factory, robots assemble cars. If 3 robots assemble 17 cars in 10 minutes, how many cars can 14 robots assemble in 45 minutes if all robots work at the same rate all the time?

3. 3 times the first of 3 consecutive odd integers is 3 more than twice the third. What is the 2nd of the 3 consecutive odd integers? I did 3(x + x + 2 + x + 4) + 3 = 2(x +4) but didn't get it.

Thanks! Appreciated if you could show me all the steps algebraically.

Answer 1

## 1.

T = position of truck, C = position of car

t = time (in minutes), notice the (t/60) because speeds are given in miles per hour. Also note the 24 minute head start.

T = 40 (t/60) + 40 (24/60)
C = 50 (t/60)

Solve when T=C

40 (t/60) + 16 = 50 (t/60)

40 t + 16×60 = 50t

16×60 = 10 t

t = 16×6 = 96 minutes (1 hour 36 minutes)

## 2

(cars built) = (robots) × (minutes) × (efficiency)

where the efficiency is how many cars a robot can build in a minute (which is likely some fraction of a car, but you get the idea). The efficiency does not vary, but everything else does, so we find that:

(cars) / (robots × minutes) = (cars) / (robots × minutes)

Plug in the values from the first situation on the left, and from the second situation on the right:

17 / (3×10) = X / (14×45)

X = 14×17×45 / 30 = 357 cars


## 3

Three consecutive odd integers can be written:

2x+1, 2x+3, 2x+5

3(2x+1) = 3 + 2(2x+5)

6x+3 = 3 + 4x + 10

2x = 10

x = 5

The second one is = 2x+3 = 13.

Check 11×3 = 33 is 3 more than 2×15 = 30.

Answer 2

1. Let truck speed be vt and car speed be vc. The truck and car will catch each other whne their position is teh same. Call position x

x = vt*(T+24/60) = vc*T -the 24/60 is the head start time in hours that the truck had.

Solve for T: (vc - vt)*T = 24/60*vt

T = 2/5 *vt/(vc-vt) = 0.4* 40/(50 - 40) = 1.6 hours

2. 3 Robot assemble 1.7 cars/minute so 1 robot cna assemble 1.7/3 cars/minute = 0.5666 cars/minute

14 robots assemble 14*1.7/3 cars /minute so in 45 minutes they assemble

45*14*1.7/3 = 15*14*1.7 = 357 car

3. 3x-3 = 2*(x+4) = 2x+8
x = 11
x+2 =13
x+4 = 15

Note 3*11 = 33 which is 30+3 = 2*15+3 so it checks

Answer 3

sorry baby, but my school year is over! i hope u get help tho