รถวิ่งจากจุด A ไปจุด B ด้วยอัตราเร็ว 60 กิโลเมตรต่อชั่วโมง

จากนั้นวิ่งกลับจากจุด B มาจุด A ด้วยอัตราเร็ว 40 กิโลเมตรต่อชั่วโมง

____

ถามว่ารถคันนี้วิ่งด้วยอัตราเร็วเฉลี่ยเท่าไร ?

เฉลย >> โจทย์ข้อนี้หลายๆคนคงจะนำ 40 + 60 แล้วหาร 2 ตอบ 50 กิโลเมตรต่อชั่วโมง
แต่คำตอบนั้นเป็นกับดักครับเพราะว่ารถวิ่งด้วยอัตราเร็ว 40 กิโลเมตรต่อชั่วโมงจะต้องใช้เวลานานกว่า
วิ่งด้วยอัตราเร็ว 60 กิโลเมตรต่อชั่วโมงแน่นอนดังนั้นเราจะนำมาเฉลี่ยแบบธรรมดาเลยไม่ได้ครับ
เราจะต้องทำการเฉลี่ยแบบถัวเฉลี่ย โดยมีวิธีการดังนี้ครับ

ก่อนอื่นให้ระยะทางทั้งหมดยาว x กิโลเมตร
จะได้ว่า ขาไปรถจะใช้เวลาวิ่งทั้งสิ้น x / 60 วินาที
และขากลับรถจะใช้เวลาวิ่งเท่ากับ x /40 วินาที

จากสูตร อัตราเร็วเท่ากับ ระยะทางหารด้วยเวลา
เมื่อเราคิดทั้งขาไปและขากลับได้ว่า
อัตรา้เร็วเฉลี่ย = ระยะทางทั้งหมด / เวลาทั้งหมด
v = ( x + x )  /  ((x / 60) + (x / 40))
v = 2x / (100x / 2400)
v = 48

ดังนั้นรถคันนี้จะมีอัตราเร็วเฉลี่ยเท่ากับ 48 กิโลเมตรต่อชั่วโมงครับ

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( x / 60 ) = ( x / 60 ) * (40 / 40) = (40x / 2400)
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ดังนั้น ( x / 60 ) + ( x / 40 ) = (40x / 2400) + (60x / 2400) = (40x + 60x) / 2400 = (100x / 2400)
ขอโืทาครับที่มาตอบช้ามาก

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ผมคิดแบบนั้นไม่เป็นอ่ะคับ ไม่เก่งคำนวน คิดง่าย ๆ แค่
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นักเรียนฝึกตอบปัยหามือใหม่คับ

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แล้ว 2400 มาได้ยังไงครับ ช่วยตอบที จาก...

(100x/2400)

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นักเรียนฝึกตอบปัยหามือใหม่คับ

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วิธีผมถูกไหมคับ จากเฉลยคับ ผมไม่รุว่า 2400 มาได้ยังไง แต่ผมเพิ่งคิดได้อ่ะคับ

v = ( x + x ) / ((x / 60) + (x / 40)

ต้องหาค.ร.น. 60กับ40 ได้ 120

ก็จะได้ (2x / 120)(3x / 120) = 5x / 120

v = 2x / (5x / 120)

240x/5x อะคับ ได้ 48 เหมือนกัน ดีใจมากเลยที่คิดได้

v = 48

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