Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Number Theory in AMC 8, 2019 Problem 16

Algebra Questions - AMC 8, 2019

Qiang drives 15 miles at an average speed of 30 miles per hour. How many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
(A) 45
(B) 62
(C) 90
(D) 110
(E) 135

Key Concepts

Algebra

Value

Average Speed


Check the Answer


Answer: is (D) 110

AMC 8, 2019, Problem 16

Try with Hints


First hint

Among the options, there is only one option which is divisible by 55 and that is 110.

That option tells the travel hour is 2.

Second Hint

Qiang drives 15 miles at an average speed of 30 miles per hour.

And we know, Average speed = Total Distance/Total Time

So, by the formula,

$\frac{15}{30} + \frac{110}{55} = \frac{5}{2}$

Final Step

In this case, If we consider the whole journey, Total Distance is (110+15)=125

And as Qiang has to drive at 50 miles per hour for the entire trip, and as Average speed = Total Distance/Total Time ,

$\frac{125}{50} = \frac{5}{2}$

As both are same , our answer 110 is established.

Subscribe to Cheenta at Youtube


Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com