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Chapter 3: Q. 3.97 (page 383)

Carina is driving from her home in Anaheim to Berkeley on the same day her brother is driving from Berkeley to Anaheim, so they decide to meet for lunch along the way in Buttonwillow. The distance from Anaheim to Berkeley is 410 miles. It takes Carina 3 hours to get to Buttonwillow, while her brother drives 4 hours to get there. The average speed Carina鈥檚 brother drove was 15 miles per hour faster than Carina鈥檚 average speed. Find Carina鈥檚 and her brother鈥檚 average speeds.

Short Answer

Expert verified

Carina鈥檚 average speed = 50 miles/hr

and her brother鈥檚 average speed = 65 miles /hr

Step by step solution

01

Step 1. Given information

Carina is driving from her home in Anaheim to Berkeley on the same day her brother is driving from Berkeley to Anaheim, so they decide to meet for lunch along the way in Buttonwillow. The distance from Anaheim to Berkeley is 410 miles. It takes Carina 3 hours to get to Buttonwillow, while her brother drives 4 hours to get there. The average speed Carina鈥檚 brother drove was 15 miles per hour faster than Carina鈥檚 average speed.

02

Step 2. Calculating speed

Let

Carina鈥檚 average speed = x miles/hr

and her brother鈥檚 average speed =x+15 miles /hr

Distance travelled by Carina = y

Distance travelled by her brother = 410-y

Now :3x=410-4(x+5)7x=350x=50

Carina鈥檚 average speed = 50 miles/hr

and her brother鈥檚 average speed = 65 miles /hr

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